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UNIVERSITY    OF   CALIFORNIA. 


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THE  THEORY  OF  THOUGHT 


A   TREATISE  ON 


DEDUCTIVE    LOGIC 


Jt. -Davis •  J 


'O  \iiv  ovv  Kara  TO  Trpay/m  Gewptiv  ra  KOIVU 
Q. — ARISTOTLE, 


NEW    YORK 
HARPER    &    BROTHERS,    PUBLISHERS 

FRANKLIN     SQUARE 


Entered  according  to  Act  of  Congress,  in  the  year  1880,  by 

HARPER    &    BROTHERS, 
In  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


PREFACE. 


LITTLE  preface  is  needed.  The  treatise  is  not  elementary 
in  the  sense  of  bringing  the  subject  within  the  grasp  of  im- 
mature minds.  This  I  believe  to  be  impracticable,  and  no 
such  profession  is  made.  It  is  elementary  in  the  sense  that  it 
begins  at  the  beginning,  supposing  the  reader  to  have  no 
previous  knowledge  of  the  subject.  Its  extent  is  such  that 
one  who  masters  its  contents  will  be  in  possession  of  the  tech- 
nical details  of  the  science,  acquainted  with  its  established 
doctrines,  and  prepared  to  study  with  profit  and  interest  ad- 
vanced treatises.  It  is,  in  general,  a  reproduction  of  the  old 
Logic.  Whatever  scorn  the  modern  student  may  have  for 
antiquity,  he  must  know  its  doctrine  respecting  Thought  if 
he  would  read  intelligently  the  recent  literature  of  the  sub- 
ject, even  that  in  sympathy  with  him,  for  it  is  permeated 
with  the  terminology  and  the  doctrines  of  the  ancient  lo- 
gicians. 

The  treatise  reverts  to  Aristotle,  and  is  largely  a  restate- 
ment of  his  theory  as  colored  by  filtration  through  mediaeval 
mind.  " Since  his  day,"  says  Kant,  "Logic  has  taken  no 
backward  step,  and  also  up  to  this  time  it  has  been  able  to 
take  no  step  forward,  and  thus,  to  all  appearance,  is  conclud- 
ed and  perfected."  A  fiery  trial  for  ages  has  neither  con- 
sumed it  nor  refined  it,  and  it  is  likely  to  remain  perpetually 
an  accepted  part  of  the  sum  of  human  knowledge.  Hence, 
in  treating  the  old  Logic,  I  have  aimed  at  clear,  correct,  and 
complete  statement  rather  than  at  any  modification.  Of 
late  years  many  innovations  have  been  proposed,  some  of 
which  are  examined  and  criticised.  Whenever  in  the  treatise 
a  new  view  is  offered,  it  is  distinctly  indicated  as  such. 


IV  PREFACE. 


A  great  number  and  variety  of  examples,  both  for  illustra- 
tion and  for  praxis,  mitigating  somewhat  the  severity  of  the 
subject,  seemed  to  me  desirable.  They  have  been  collected 
from  every  available  source  ;  some  are  ancient,  some  modern, 
many  are  newly  invented. 

I  have  used  with  great  freedom  standard  authors,  keeping 
constantly  at  hand  Arnauld,  Whately,  Hamilton,  Mansel, 
Thomson,  De  Morgan,  Mill,  and  Bain,  and  a  dozen  or  more 
school-book  writers,  profited  by  their  research,  and  adopted 
their  views  and  phraseology  whenever  it  seemed  advantage- 
ous. Abundant  references  to  them,  together  with  this  gen- 
eral acknowledgment,  will,  I  hope,  be  deemed  sufficient.  I 
have  not  sought  to  embellish  the  margin  with  recondite  mat- 
ter, but  have  added  many  references  to  other  accessible  works, 
hoping  to  lead  the  reader  into  yet  wider  fields. 

The  treatise  has  been  prepared  with  much  pains.  That 
there  are  no  blunders  in  it  would  be  too  much  to  hope,  but 
it  is  sent  to  its  account  with  all  its  imperfections  on  its  head. 
If,  on  the  whole,  it  is  a  good  book,  it  will  live  and  be  useful  ; 
if  not,  it  will  die,  the  sooner  the  better. 


K.  DAVIS. 

UNIVERSITY  OF  VIRGIMA. 


CONTENTS. 


PART   FIRST.— INTRODUCTORY. 

I.  DEFINITION  OF  LOGIC.  Paga 

§  1.  Definition,  and  tb  3  word  Logic 1 

§  2.  Science. — Logic  not  an  Art 2 

§  3.  Thought  the  Object-matter  of  Logic 4 

§  4.  Forms  of  Thought 5 

§  5.  Necessary  Forms. — Psychology  Distinguished 6 

§  6.  Theory  of  Thought 1 

§  7.  Free  Treatment  Adopted 8 


II.  PRIMARY  LAWS. 

§  1.  Their  Origin  and  General  Character 9 

§  2.  The  Law  of  Identity 10 

§  3.  The  Law  of  Contradiction 11 

§4.  The  Law  of  Excluded  Middle 13 

§  5.  These  Laws  are  Complementary  and  Co-ordinate 14 

§  6.  Only  a  Negative  Criterion  of  Reality. — The  Absolute 15 

§  7.  The  Principle  of  Sufficient  Reason 16 

§  8.  The  Postulate  of  Logic 17 


PART  SECOND.— OF  CONCEPTS. 
I.  THE  TERM. 

§  1.  General  Divisions  of  Logic 19 

§  2.  Abstraction.— Kinds  of  Marks 19 

§  3.  Generalization  and  Specialization 20 

§  4.  Conception,  Individual  and  General 22 

§  5.  Realization  of  Concepts 24 

§  6.  These  Acts  Imply  Each  Other 25 

§  7.  Abstractions 25 

§  8.  Language. — Symbolic  Thinking 27 


VI  CONTENTS. 


II.  QUALITY. 

Page 

§  1.  The  Four  Views  to  be  Taken  of  Concepts 30 

§  2.  The  Leibnitzian  Analysis  of  Knowledge 30 

§  3.  Obscure  and  Clear 31 

§  4.  Confused  and  Distinct 31 

§  6.  Inadequate  and  Adequate 32 

§  6.  Intuitive  and  Symbolic 33 

§  7.  Perfect  Knowledge 34 

III.  QUANTITY. 

§  1.  Intension  and  Extension 35 

§  2.  The  Law  of  these  Quantities 36 

§  3.  The  Quantity  of  an  Abstraction 37 

§  4.  The  Coexistence  of  the  Quantities 38 

IV.  RELATION. 

§  1.  In  Intension, — Identical  and  Different 40 

§  2.  Congruent,  Incongruent,  and  Conflictive 40 

§  3.  Involved  and  Co-ordinate 42 

§  4.  Relations  in  Extension 42 

§  6.  Subordination. — Genera  and  Species 43 

§  6.  Correspondencies 45 

§  7.  Correlative  Terms 45 

§  8.  First  and  Second  Intentions 46 

.     V.  DEFINITION. 

§  1.  The  Intensive  View 48 

§  2.  The  Scholastic  View 49 

§  3.  Intersection  of  Concepts 50 

§  4.  Kinds  of  Definitions 50 

§  5.  Rules 52 

§  6.  Praxis 54 

VI.  DIVISION. 

§  1.  Definition  and  Division  Contrasted 50 

§  2.  Two  Kinds  of  Wholes 50 

§  3.  Co-ordination. — Dichotomy 57 

§  4.  The  Principle  of  Division 58 

§  5.  Trichotomy  and  Polytomy 59 

§  6.  Canon  and  Rules 60 

$  7.  Praxis 62 


CONTENTS.  Vll 


VII.  COMPLETE  SYSTEM.  Paga 

§  1.  Scheme  of  the  Two  Quantities 64 

§  2.  Tree  of  Porphyry ._ 65 

§  3.  Sumraum  Genus. — The  Categories 66 

§  4.  Infima  Species.— The  Individual 68 

§  5.  Extent  of  the  Series 69 

§  6.  Definitions  and  Divisions  Convertible 70 

§  7.  The  Logic  of  Common  Systems 71 

§  8.  The  Logic  of  Scientific  Systems 72 

§  9.  The  Primary  Laws  Applied 74 


PART  THIRD.— OF  JUDGMENTS. 
I.  THE  PROPOSITION. 

§  1.  Judgment  Defined. — A  Return 75 

§  2.  Parts  of  the  Proposition.— The  Subject 76 

§  3.  The  Copula 77 

§  4.  The  Strict  Logical  Form 78 

§  5.  The  Predicates 79 

§  6.  Judgments,  Intensive  and  Extensive 80 

§  7.  Categorical  and  Conditional 82 

§  8.  Total  and  Partial 82 

§  9.  Positive  and  Negative 85 

§  10.  Symbols  of  Quantity  and  Quality 88 

§  1 1.  Propositions,  Simple,  Complex,  and  Compound 89 

§  12.  Judgments,  Analytic  and  Synthetic 93 

§  13.  Judgments  of  Degree 94 

§  14.  Praxis 100 


II.  INFERENCES. 

§  1.  Divisions. — Immediate  Inference 102 

§  2.  Implied  Judgment  Discriminated. 103 

§  3.  A  General  Rule 104 

§  4.  Active  and  Passive 104 

§  5.  Added  Determinants  and  Complex  Conceptions 104 

§  6.  Infinitation 105 

§  7.  Conversion 106 

§  8.  Opposition 108 

89.  Praxis..,  .  113 


Yin  CONTENTS. 


III.  INNOVATIONS.  Page 

§  1.  Many  Proposed 115 

§  2.  The  Semi-definite  "Some" 115 

§  3.  Quantification  of  the  Predicate. — Table 116 

§  4.  The  New  Forms,  their  Occurrence 118 

§  5.  Proved  to  be  Compounded 120 

§  6.  Mathematical  in  Character 123 


PART  FOURTH.— OF  REASONINGS. 
I.  THE  SYLLOGISM. 

§  1.  Its  Definition 125 ' 

§  2.  Its  Parts,  and  their  Order , 130 

§  3.  Its  Various  Kinds 133 

§  4.  The  Canon 137 

§  5.  General  Rules 139 

II.  FIGURE  AND  MOOD. 

§  1.  Conspectus  of  Figure 1-14 

§  2.  Reasonings  in  the  Second  and  Third  Figures 145 

§  3.  The  Moods  Evolved 148 

§  4.  Names  of  the  Moods 148 

§  5.  Reduction 150 

§  6.  Equivalent  Moods 154 

§  7.  The  Fourth  Figure. . -. 156 

§  8.  The  Syllogism  Vindicated 158 

§  9.  Praxis 165 

III.  QUANT1TATIVES. 

§  1.  Syllogisms  of  Equivalence 170 

§  2.  Mathematical  Demonstration 173 

§  3.  Reduction  to  Qualitatives 175 

§  4.  Syllogisms  of  Comparison 176 

§  5.  Hamilton's  Unfigured  Syllogism 178 

§  6.  The  Causal  Syllogism 179 

§  7.  Praxis 180 

IV.  COMPOUND  AND  DISGUISED  FORMS. 

§  1.  Irregularities. — The  Enthymeme 183 

§  2.  The  Epichirema 186 


CONTENTS.  IX 

Pag. 

§  3.  The  Sorites 187 

§  4.  Resolution  of  Arguments 180 

§  5.  Syllogisms  having  Compound  Premises 194 

§  6.  Syllogisms  having  Irregular  Premises 190 

§  7.  Modes  of  Arguing  Named 398 

§  8.  Praxis 200 

V.  CONDITIONALS. 

§  1.  Divisions 200 

§  2.  Conjunctives .' 200 

§  3.  Disjunctives 207 

§  4.  Conjunctive-disjunctives 209 

§  5.  Conjunctive  Syllogisms 211 

§  G.  Disjunctive  Syllogisms 213 

§  7.  Conjunctive-disjunctive  Syllogisms 215 

§  8.  The  Dilemma 217 

§  9.  Praxis 220 

VI.  ANALYSIS   OF   CONDITIONALS. 

§  1.  The  Question,  and  Order  of  Discussion ;  225 

§  2.  Real  and  Ideal  Thought 226 

§  3.  First  Prepositional  Use  of  Contingent  Hypothetical 229 

§  4.  Second  Prepositional  Use 232 

§  5.  Reasonings  Founded  on  these  Uses 235 

§  0.  Reasonings  Implied  in  the  Second  Use 237 

§  7.  The  Unreal  Hypothetical 242 

§  8.  Conjunctive  Syllogisms  are  not  Inferences 245 

§  9.  Other  Conditional  Syllogisms  are  not  Inferences 249 

§  10.  Summary  of  Doctrine 250 


PART  FIFTH.—  OF   FALLACIES. 
I.  DISTRIBUTION. 


§  1.  Treatment  of  Fallacies  Justified 
§  2.  Bacon's  Idols 


. 

253 

§  3.  Mill's  Classification  ..................................................  254 

§  4.  Whately's  Classification  .............................................  255 

§  5.  Aristotle's  Classification  .......................................  ......  256 

§  0.  Paralogisms  .........................................................  258 

II.  SOPHISMS  IN  DICTION. 

§  1.  Their  Common  Fault  ................  =.  ...............................  261 

§  2.  Of  Equivocation  .......................   .............................  261 


X  CONTENTS. 

Page 

§  3.  Of  Amphiboly. 266 

§  4.  Of  Composition  and  Division 267 

§  5.  Of  Accent 268 

§  6.  Of  Figure  of  Speech. 270 

III.  SOPHISMS  IX  MATTER. 

§  1.  Of  Accident 272 

§  2.  Of  Absolute  and  Limited  Terms 273 

§  3.  Of  Ignoring  the  Refutation 276 

§  4.  Of  Antecedent  and  Consequent 280 

§  5.  Of  Begging  the  Question 282 

§  6.  Of  False  Cause 290 

§  7.  Of  Many  Questions 294 

IV.  EXAMPLES. 

§  1.  Inexplicable  Fallacies 290 

§  2.  The  Achilles 296 

§  3.  The  Diodorus  Cronus 298 

§  4.  The  Litigiosus 299 

§  5.  The  Mentions 300 

§  6.  The  Sorites ' 301 

§  7.  The  Ignava  Ratio 302 

§  8.  Praxis 305 


LOGIC, 


OR 


THE   THEORY   OF   THOUGHT. 


PAET  FIRST.— INTRODUCTORY. 


I.  DEFINITION  OF  LOGIC. 

§  1.  Logic  is  the  science  of  the  necessary  forms  of  thought. 

The  word  "  Logic  "  is  derived  from  the  Greek  Xoyto/,  an  adjective 
qualifying  £7rtorr//t^  (science)  or  Trjoay^m'a  (matter  of  study)  under- 
stood. The  meaning  of  Xoyto/  and  of  its  original,  Xoyoc,  is  ambigu- 
ous. The  latter  is  equivalent  to  both  the  ratio  and  the  oratio  of  the 
Latins,  to  thought  and  to  speech.  This  ambiguity  passed  into  the  de- 
rivative, and  has  affected  the  views  of  many  logicians  as  to  the  object- 
matter  of  the  science,  some  holding  that  it  treats  of  words  or  language 
rather  than  of  thought.1 

Aristotle  did  not  designate  by  the  term  Xoyuv/  the  science  whose 
doctrine  he  first  fully  developed.  The  terms  Analytic,  Apodeictic, 

1  See  Hamilton's  Logic,  p.  3.  It  may  be  well  to  note  at  the  outset  that  logicians 
are  divided  into  three  schools,  according  as  they  hold  words,  things,  or  conceptions 
to  be  the  subject  of  Logic ;  and  these  are  entitled,  respectively,  the  Verbal,  the 
Phenomenal,  and  the  Conceptional  Schools.  The  first  is  represented  by  many 
scholastics,  by  Hobbes,  Whately,  and  De  Morgan.  The  second  numbers  Bacon, 
Helvetius,  Comte,  J.  S.  Mill,  and  Bain  among  its  chief  expositors.  At  the  head 
of  the  third  is  Kant,  followed  by  Krug,  Esser,  and  the  recent  German  logicians 
generally,  and  by  Hamilton  and  Mansel  with  their  train  of  Scotch  and  English  pu- 
pils ;  to  whom  may  be  added  most  French  writers,  following  Arnauld.  The  present 
treatise  takes  the  Kantian,  or  conceptualist,  view.  Logic  treats  of  thought.  But 
as  thought  is  always  about  things,  and  is  expressed  in  words,  Logic  cannot  proceed 
in  entire  disregard  of  these,  but  should  constantly  keep  them  subordinate.  See 
Cretiens's  Logical  Method,  ch.  v.  Oxford,  1848. 

1 


2  INTRODUCTORY. 

and  Topic  (the  latter  equivalent  to  Dialectic,  and  including  Sophistic) 
were  special  names  by  which  he  denoted  parts  or  applications  of  Logic. 
He  used  no  one  term  to  designate  the  whole  science.  Plato  used 
the  term  Dialectic  to  denote  more  than  Logic  proper  includes,  while 
Aristotle  used  it  to  denote  less,  and  it  is  usually  regarded  as  the  most 
ancient  synonym  for  Logic.  With  whom  the  designation  Logic  origi- 
nated does  not  appear ;  but  it  is  ancient,  being  used  by  Cicero,  and 
is  attributed  by  Boethius  to  the  early  Peripatetics. 

§  2.  "  A  Science  is  a  complement  of  cognitions,  having,  in  point  of 
form,  the  character  of  logical  perfection ;  in  point  of  matter,  the  char- 
acter of  real  truth."3  The  logical  perfection  of  a  branch'  of  knowledge 
is  attained  by  systematically  arranging  and  exhibiting  its  object- 
matter,  clearly,  distinctly,  completely,  and  in  harmonious  connection. 
This  implies  classification.  Again,  the  object-matter  of  a  science  must 
be  real  truth,  otherwise  it  cannot  be  said  to  be  known ;  what  is  unreal 
or  false  cannot  be  a  constituent  of  a  science.8  Hence  the  definition 
may  be  conveniently  abbreviated  thus :  A  Science  is  a  perfected  sys- 
tem of  real  truths;  or  thus:  Science  is  classified  knowledge.  Few 
branches  of  knowledge  have  reached  this  ideal  perfection  ;  if  not  the 
mathematics,  none  have  done  so.  But  since  in  many  departments 
knowledge  has  far  outgone  its  crude  beginnings,  and  made  great 
progress  towards  this  ideal,  such  branches  are  properly  called  sciences. 

"  The  distinction  between  science  and  art  is,  that  science  is  a  body 
of  principles  and  deductions  to  explain  some  object-matter ;  an  art  is 
a  body  of  precepts,  with  practical  skill,  for  the  completion  of  some 
work.  A  science  teaches  us  to  know,  an  art  to  do ;  the  former  de- 
clares that  something  exists,  with  the  laws  and  causes  which  belong  to 
its  existence;  the  latter  teaches  how  something  must  be  produced."4 
In  science  scimus  ut  sciamus  ;  in  art  scimus  ut  producamus.  Science 
discovers  laws ;  art  gives  rules.  Uepi  yeveaiv  Ti\rr),  TTEJOI  TO  ov  ITTHTTI]- 
/i»j.6  This  distinction  holds  good,  in  reference  to  the  extremes,  as  to 
pure  speculative  sciences  and  mere  manual  arts.  But  science  often 
leads  so  directly  into  art,  and  art,  except  in  its  rudest  forms,  is  so  de- 
pendent on  science,  that  usually  they  cannot  be  set  clearly  apart. 

3  Hamilton's  Logic,  p.  335. 

3  Scientific  knowledge  (TO  iiritsTavQai),  except  when  of  axiomatic  principles 
(VOEIV),  requires  a  conviction  of  the  truth  of  the  given  proposition,  and  a  knowl- 
edge of  its  reason  or  cause. — Aristotle's  Anal.  Post,  i,  2, 1. 

4  Thomson's  Outline  of  the  Laws  of  Thought,  §  6.  *  Aristotle. 


DEFINITION    OF   LOGIC. 


Moreover,  there  is  a  body  of  practical  sciences,  e.g.  Ethics,  Economies, 
etc.,  that  occupy  intermediate  ground,  and  yet  are  never  called  arts; 
others  again,  e.  g.  Rhetoric,  Grammar,  etc.,  are  commonly  viewed  as 
arts.8 

Some  logicians  have  viewed  Logic  as  an  art,  and  entitled  it  The  art 
of  thinking  (Arnauld 7) ;  The  art  of  reasoning  (Aldrich) ;  The  right 
use  of  reason  (Watts),  etc.  Others  pronounce  it  to  be  both,  thus : 
Ars  artium,  et  scientia  scientiarum  (Duns  Scotus,  13th  century);* 
The  art  and  science  of  reasoning  (Whately) ;  The  art  of  thinking, 
which  means,  of  correct  thinking,  and  the  science  of  the  conditions 
of  correct  thinking  (Mill0).  The  extreme  view  of  Logic  as  an  art 
is  that  it  teaches  us  how  to  think.  This  is  evidently  absurd.  A 
course  in  Logic  is  about  as  needful  for  making  men  thinkers  as  a 
course  in  Ethics  is  to  make  them  virtuous,  or  a  course  in  Optics  to 
make  them  see.  A  modified  view  is  that  Logic  teaches  us  how  to 
think  correctly,  or,  negatively,  how  to  avoid  fallacy,  or  that  it  teaches 
how  to  test  the  validity  of  given  arguments.  If  such  is  the  scope 
and  object  of  Logic,  it  may  be  set  aside  as  of  little  or  no  value,  con- 
sisting of  a  system  of  rules  which  the  initiated  never  use  and  the  un- 
initiated never  miss.  Such  views  have  historically  brought  Logic  into 
great  discredit,  just  as  Chemistry  was  brought  into  disrepute  by  the 
extravagant  pretensions  of  the  alchemists.10 

But  Logic  is  not  primarily,  nor  even  secondarily,  an  art.  It  is 
strictly  a  science ;  the  science  teaching  how  we  do  think  and  how  we 
must  think  if  we  think  correctly.  It  is  the  theory  of  reasoning ;  or, 
better,  it  is  the  theory  of  thought.  The  difference  between  Logic 
and  an  Art  of  Thinking  is  similar  to  that  between  Anatomy  and  Sur- 
gery. The  value  of  Logic  is  such  as  belongs  to  pure  science,  which, 
in  this  day,  needs  no  demonstration.  It  is  something  of  profoundcst 
interest  to  know  what  are  the  mental  processes  in  the  intellectual  act 
of  thinking,  and  of  such  matter  the  liberal  mind  asks  primarily,  Is  it 
true?  not,  Is  it  useful?  Knowledge 'is  power,  but  we  have  to  do 


fi  See  Hamilton's  Sfefapkysic*,  pp.  81-84. 

7  I}Art  de  Penser,  1662,  that  most  admirable  work,  known  commonly  as  the 
"  Port-Royal  Logic." 

8  See  Hamilton's  Logic,  p.  26.  9  Ex.  of  Hamilton's  Phil.  vol.  ii,  p.  149. 

10  See  Locke's  contemptuous  opinion  of  Logic,  Essay,  bk.  iv,  ch.  xvii.  Also 
Goethe's,  in  Faust,  pt.  i,  speech  of  Mephistopheles  to  "  der  Schuler."  It  may  be 
objected  that  this  is  merely  the  mocking  gibe  of  Mephistopheles;  but  cf.  in  Wahr. 
und  Dicht.  pt.  i,  bk.  iv. 


4  INTRODUCTORY. 

with  it  here  as  knowledge,  not  as  power.  Where,  however,  one  has 
mastered  the  science,  there  is  a  practical  result  in  a  special  cultivation 
of  his  reasoning  powers ;  and,  moreover,  whatever  process  one  clearly 
understands,  it  is  manifest  he  can  more  clearly  and  efficiently  per- 
form.11 

The  Greek  Aristotelians,  and  after  these  the  scholastic  Aristotelians, 
subdivided  Logic  into  what  the  latter  called  Logica  docens  and  Logica 
utens.  The  former  is  explained  as  an  abstract  theory  of  thought — 
guce  tradit  proecepta ;  the  latter  as  a  concrete  practice,  as  an  applica- 
tion of  these  rules  to  use — quce  utitur  prceceptis.  Hamilton,  follow- 
ing Kant,  calls  the  former  "  General  or  Abstract  Logic,"  the  latter 
"  Special  or  Concrete  Logic."  The  former  only  is  Logic ;  the  latter, 
quite  properly  called  "Applied  Logic,"  and  treating  chiefly  of  the 
methods  by  which  particular  sciences  should  be  logically  developed, 
is  no  part  whatever  of  the  science  of  Logic,  of  Logic  proper,  and  ac- 
cordingly will  be  disregarded  in  the  present  treatise.13 

§  3.  The  object-matter  of  Logic  is  thought.  Thus  it  is  distin- 
guished from  other  sciences,  each  of  which  has  its  own  special  object- 
matter.  Astronomy  treats  of  the  stars ;  geology,  of  the  earth's  crust ; 
zoology,  of  its  fauna ;  botany,  of  its  flora ;  mathematics,  of  quantity  ; 
theology,  of  God ;  philosophy,  of  principles ;  psychology,  of  mind ; 
ethics,  of  morals,  etc. ;  so  Logic  treats  of  thought.  Thought  denotes 
only  the  acts  of  the  understanding,  as  distinguished  from  perception, 
memory,  feeling,  desire,  volition,  of  whose  exercises  Logic  takes  no  ac- 
count. Thought  may  be  simply  defined  as  the  cognition  of  one  no- 
tion in  or  under  another.  Hence  in  this  act  we  are  said  to  compre- 
hend or  understand  a  thing.  E.  g.,  A  book  lies  before  me.  I  may 
be  conscious  of  the  impression  the  thing  makes  without  cognizing 
what  it  is.  This  is  mere  perception.  But  if  I  cognize  what  it  is, 
and  say,  "  It  is  a  book,"  I  have  brought  it  under  a  certain  class  or 
concept  of  things  which  we  call  "  book."  This  is  thought.13  Now 
we  think  about  all  conceivable  things,  but  all  of  these  are  to  Logic 
perfectly  indifferent  except  one,  that  is,  thought  itself.  In  Logic  we 
think  about  thought.  What  thought  involves,  Logic  evolves.14 

11  See  Hamilton's  Logic,  pp.  7,  8  ;  and  McCosh's  Logic,  pt.  iii,  §  80. 

"  Hamilton's  Logic,  p.  38,  and  p.  42.  13  Id.  pp.  9, 10. 

"  See  Aristotle,  De  Soph.  Elench.  ix.  Sciences  and  demonstrations,  says  he,  are 
possibly  infinite,  and  would  require  omniscience  to  treat  them.  The  dialectician 
has  to  discover  only  the  principles  common  to  all  spheres  of  thought. 


DEFINITION    OF    LOGIC. 

§  4.  W^e  observe,  then,  that  Logic  does  not  at  all  concern  itself 
with  what  things  thought  considers.  It  treats  of  thought  regardless 
of  its  content.  It  is  usual  to  express  this  by  saying  that  Logic  treats 
of  the  forms  of  thought  abstractly,  i.  e.  excluding  its  matter.  The 
form  of  thought  as  distinguished  from  its  matter  may  be  exemplified 
thus:  When  I  think  that  the  book  before  me  is  a  folio,  the  matter 
of  this  thought  is  "  book ;"  and  "  folio,"  the  form  of  it,  is  "  a  judg- 
ment." The  forms  of  thought  may  be  represented  as  empty  shells, 
into  which  very  various  matter  may  enter  as  the  content  of  thought ; 
or  as  mere  outlines,  to  which  different  substances  may  conform,  like 
as  a  statue  may  be  formally  the  same  whether  of  wood,  metal,  or 
marble.  So  the  science  Morphology  treats  of  the  forms  of  plants  and 
animals,  and  Crystalology,  an  abstract  geometrical  science,  treats  only 
of  the  forms  of  minerals.  The  matter  and  the  form  have,  of  course, 
no  separate  existence.  No  object  is  cogitable  except  under  some 
form  of  thought ;  and  no  form  of  thought  can  have  any  existence  in 
consciousness  unless  some  object  be  thought  under  it.  But  by  ana- 
lytic abstraction  we  can  consider  these  apart ;  we  can  consider  either 
the  object  thought,  or  the  manner  of  thinking  it ;  we  can  distinguish 
the  matter  from  the  form  of  thought.  Now  it  is  the  form  of  thought, 
abstracting  its  matter,  that  Logic  considers.  Modern  logicians  arc 
fond  of  saying  that  all  matter  is  extralogical.  This  might  be  under- 
stood to  represent  Logic  as  a  science  without  a  content,  without  mat- 
ter of  its  own.  But  Logic,  like  every  other  science,  has  its  own  special 
content.  Its  object-matter  is  thought ;  all  other  matter  is  extralogical. 
Its  object-matter  is  thought  discharged  of  its  matter ;  i.  e.,  it  is  the 
form  of  thought. 

Logic,  then,  is  properly  an  abstract  science,  one  abstracting  from 
each  and  all  the  sciences,  and  considering  only  what  is  common  to  all ; 
i.  e.  the  formal  thought  to  which  all  are  subjected,  and  making  that 
its  object-matter.  Hence  Logic  is  in  a  similar  and  equal  relation  to 
all  sciences,  and  fundamental  to  all.  Now  philosophy  is  the  science 
of  principles,  and  is  therefore  the  fundamental  science  in  the  sense 
that  its  object-matter  is  the  primary  truths  that  underlie  all  knowl- 
edge. But  philosophy  proceeds  logically  or  not  at  all.  Hence  Logic 
is  fundamental  even  to  philosophy  in  the  sense  that  it  exhibits  the 
necessary  processes  of  thought  which  bind  philosophy  as  well  as  every 
other  science.  Moreover,  Logic  is  itself  bound  to  proceed  logically, 
and  can  become  a  science  only  by  conforming  to  those  processes 
which  it  is  its  province  to  explicate  and  exhibit. 


6  INTRODUCTORY. 

Let  it  not,  however,  be  supposed  that  Logic  treats  of  thought  only 
as  exercised  and  displayed  in  scientific  pursuits.  It  treats  of  thought 
universally.  Thought  as  exhibited  in  all  kinds  of  literature  and 
speech,  in  common  conversation,  in  silent  meditation  ;  all  our  common 
every-day  thinking,  about  the  most  trivial  things  and  at  every  instant, 
is  formally  all  of  the  same  nature,  proceeds  in  the  same  manner,  is 
governed  by  the  same  laws,  is  logical  if  correct.  Consequently,  illus- 
trations of  the  principles  of  Logic  are  to  be  drawn  not  merely  from  any 
of  the  sciences,  but  from  any  kind  of  knowledge,  wherein  anything 
whatever  becomes  an  object  of  thought.  Logic  teaches  or  explains 
how  any  human  mind  rightly  thinks  at  any  time  about  anything. 

§  5.  To  define  Logic  as  the  science  of  the  forms  of  thought  would 
not  be  sufficient  to  set  it  entirely  apart,  would  not  discriminate  clearly 
its  character.  Psychology  is  inter  alia  a  science  of  formal  thought, 
and  needs  to  be  distinguished  from  Logic.  Psychology  is  an  empir- 
ical science ;  it  is  evolved  from  experience.  It  is  therefore  an  induc- 
tive, natural  science,  one  a  posteriori.  It  systematizes  the  conscious 
mental  activities,  and  points  out  their  laws.  In  dealing  with  the  fac- 
ulty of  thought,  it  explains  the  modes  in  which  we  think,  teaching 
how  we  do  think,  and  refers  for  the  test  of  its  doctrine  to  the  reflect- 
ive consciousness  of  every  individual. 

Logic,  on  the  other  hand,  if  taken  in  its  strictest  sense,  is  not  at 
all  an  empirical,  but  a  speculative  or  theoretical,  science.  It  accepts 
from  Psychology,  or  obtains  by  the  analysis  of  given  products  of 
thought,  certain  primary  laws ;  from  these  it  deduces  secondary  laws 
of  thought,  and  thus  proceeds  to  demonstrate  the  necessary  processes 
of  thought,  those  we  must  follow  in  thinking  correctly.  It  is  there- 
fore a  purely  deductive  science,  one  a  priori.  It  teaches  not  how  we 
do  think,  as  a  matter  of  fact,  but  how  we  must  think,  as  a  matter  of 
necessity,  if  the  thinking  be  consequent.  It  appeals,  not  to  conscious- 
ness, but  to  demonstration,  in  support  of  its  truthfulness. 

Psychology,  then,  is  the  natural  history  of  thought ;  Logic  is  the 
theory  of  thought.  Psychology  considers  thought  as  an  operation ; 
Logic  considers  it  as  a  product.  Psychology  treats  of  conceiving, 
judging,  reasoning ;  Logic  treats  of  concepts,  judgments,  reasonings. 
Psychology  treats  of  thought  as  it  is ;  Logic  of  thought  as  it  must  be. 
Psychology  teaches  how  we  do  think,  Logic  teaches  how  we  must 
think.  The  one  treats  the  forms  of  thought  merely  as  actual,  the 
other  proves  them  necessary.  Like  mathematics,  Logic  is  purely  de- 


L 


DEFINITION    OF    LOGIC.  7 

monstrative.  Indeed,  in  respect  of  their  demonstrative  character, 
"  Logic  and  Mathematics  stand  alone  among  the  sciences,  and  their 
peculiar  certainty  flows  from  the  same  source.  Both  are  conversant 
about  the  relations  of  certain  a  priori  forms  of  intelligence — Mathe- 
matics about  the  necessary  forms  of  imagination,  Logic  about  the 
necessary  forms  of  understanding.  Both  are  thus  demonstrative  or 
absolutely  certain  sciences,  each  developing  what  is  given  as  neces- 
sary in  the  mind  itself."  1  Hence  Kant,  followed  by  Esser,  who  in 
turn  is  followed  by  Hamilton,  defines  Logic  to  be  the  science  of  the 
necessary  forms  of  thought.18 

Such  is  the  definition  of  Pure  Logic.  It  excludes  Psychology. 
We  have  already  seen  that  it  excludes  Applied  Logic.  If  we  adhere 
to  it,  we  must  reject  also  Modified  Logic  as  not  properly  any  part  of 
the  science.  For  Modified  Logic  considers  thought  "not  as  deter- 
mined by  its  necessary  and  universal  laws,  but  as  contingently  affect- 
ed by  the  empirical  conditions  under  which  thought  is  actually  exert- 
ed, showing  what  these  conditions  are,  how  they  impede,  and,  in  gen- 
eral, modify  the  act  of  thinking ;  and  how,  in  fine,  their  influence 
may  be  counteracted."  l  Treatises  on  Concrete  or  Applied  Logic, 
and  on  Modified  Logic,  may  be  valuable  appendices  to  works  on 
Logic,  but  they  constitute  no  part  of  the  pure  science.18 

§  6.  As  an  expressive  synonym  for  Logic  we  have  adopted  the 
phrase  "  Theory  of  Thought."  Theory  is  properly  opposed  to  prac- 
tice. Theory  is  mere  knowledge ;  practice  is  the  application  of  it.1" 


15  Hamilton's  Logic,  p.  31. 

16  It  will  be  seen  hereafter  that  the  u  necessary  forms  of  thought "  corresponds 
to  the  old  logical  phrase  "  second  intentions."     Hence  an  excellent  definition  of 
Logic,  were  not  the  phrase  obscure,  would  be  "  the  science  of  second  intentions.'* 
See  pt.  ii,  ch.  iv,  §  8. 

17  Hamilton's  Logic,  p.  43. 

18  On  the  title-page  occurs  the  phrase  "  Deductive  Logic,"  to  indicate  the  absence- 
of  any  treatment  of  Induction  in  the  present  work.     The  importance  of  Induction 
cannot  be  overestimated,  but  it  calls  for  a  distinct  treatise.     We  often  hear  the 
phrase  "  Inductive  Logic."    But  induction  is  not  correctly,  etymology  apart,  op- 
posed to  Deduction,  and  all  Logic  proper  is  Deductive  Logic. 

19  With  Plato  &wpttV  is  applied  to  a  deep  contemplation  of  the  truth.    By  Aris- 
totle it  is  always  opposed  to  Trpdmiv,  and  to  TTOIEU',  so  that  he  makes  philosophy 
tlieoretical,  practical,  and  artistical.     The  Latins  and  Boethius  rendered  fowpclt/  by 
speculari. — Trendelenburg's  Element.  Log.  Arist.  p.  76.     See  also,  on  theory  and 
practice,  Hamilton's  Metaphysics,  p,  120. 


8  INTRODUCTORY. 

Theory  denotes  the  most  general  laws  to  winch  certain  facts  can  be 
reduced.  It  is  a  collection  of  the  inferences  drawn  from  facts  and 
compressed  into  principles ;  it  is  a  systematized  explanation  of  facts 
demonstrably  true.  Logic  is  such  a  systematized  collection  of  the 
laws  that  govern  thinking,  and  it  is  occupied  with  demonstrating 
their  validity  from  certain  axioms.  It  is,  therefore,  properly  called 
the  Theory  of  Thought. 

§  Y.  It  is  evident  that  a  work  strictly  limited  by  the  definition  of 
pure  Logic  would  be  very  abstract  and  difficult.  Being  a  discussion 
of  forms,  it  could  offer  no  examples ;  for  since  a  pure  abstract  form 
cannot  be  realized  in  consciousness  apart  from  matter,  much  less  can 
it  be  expressed.  Even  in  general  expressions  by  algebraic  symbols, 
the  symbols  themselves  are  a  species  of  matter  that  is  extralogical. 

Again,  if  the  treatise  be  kept  strictly  apart  from  Psychology,  it 
will  admit  of  no  reference  to  actual  thinking.  It  will  tell  us  noth- 
ing of  how  the  mind  does  actually  proceed  in  its  efforts  to  systema- 
tize its  knowledge,  nothing  of  the  nature  of  the  thinking  act  as  giving 
rise  to  the  logical  product,  nothing  of  the  phenomena  of  illegitimate 
thinking.  Thus  our  science  would  be  shorn  of  its  rays. 

Consequently,  few,  if  any,  writers  have  allowed  themselves  to  be  rig- 
idly bound  by  the  definition.  In  the  present  treatise,  while  we  make 
pure,  abstract  Logic  its  basis,  while  developing  systematically  the  The- 
ory of  Thought,  and  keeping  this  prime  object  constantly  in  view,  we 
shall  freely  transgress  the  limits  of  the  definition  whenever  it  seems 
desirable.  We  shall  consider  not  merely  how  the  mind  must  think, 
but  how  it  does  think.  We  shall  give  copious  concrete  illustrations, 
and  analyze  and  exhibit  actual  exercises  of  thought,  appealing  to  ob- 
servation and  to  the  experience  of  consciousness  to  corroborate  the 
theory,  just  as  the  astronomer  turns  to  the  stars  to  observe  the  ful- 
filment of  the  laws  of  the  Mecanique  Celeste. 


PRIMARY    LAWS. 


II.  PRIMARY  LAWS. 

§  1.  In  the  study  of  Psychology  we  find  by  subjective  analysis  that 
there  are  certain  modes  of  intelligence  to  which  the  mind  is  necessi- 
tated by  virtue  of  its  essential  and  original  constitution.  Among 
others  are  certain  forms  of  thought  determined  or  necessitated  by  the 
nature  of  the  thinking  subject  itself.  The  chief  of  these  necessary 
forms  are,  the  concept,  the  judgment,  the  reasoning.  By  saying  that 
these  forms  are  necessary  is  meant  that  the  mind  cannot  truly  think 
except  in  them.  But  since  they  are  native  and  necessary,  they 
must  be  universal,  both  in  the  sense  that  they  are  found  in  every 
human  mind,  and  in  the  sense  that  all  the  thoughts  of  each  mind  are 
always  determined  in  them.  For  it  cannot  be  that  a  form  is  neces- 
sary on  some  occasions  and  not  on  others.  If  so,  it  would  be  merely 
contingent,  which  contradicts  our  notion  of  necessity.  Now,  the 
forms  being  necessary  and  universal,  we  may  view  them  as  governed 
by  necessary  laws.  These  laws  will  be  an  expression  of  the  general 
abstract  principles  common  to  the  forms,  and,  as  the  result  of  a  com- 
plete analysis,  will  be  ultimate  and  axiomatic.  When  evolved  and 
enunciated,  they  are  known  as  Logical  Principles,  or  as  the  Primary 
or  Fundamental  Laws  of  Thought.1 

Again,  if,  preliminary  to  pure  Logic,  products  of  thought  viewed 
objectively  as  embodied  in  language  are  subjected  to  a  critical  anal- 
ysis, they  are  found  to  exhibit  general  or  universal  forms.  In  other 
words,  if  from  the  various  manifestations  of  thought  in  speech  and 
literature  we  abstract  the  matter  and  all  differences  characterizing 
them,  we  discover  a  residuum  common  to  all,  a  mode,  a  manner,  hav- 
ing certain  forms  that  belong  to  all,  that  interpenetrate  all.  These 
forms,  being  universal,  are  considered  as  governed  by  laws ;  and  these 
laws,  when  enunciated,  are  found  to  be  the  same  as  those  obtained  by 
subjective  analysis.  Thus  the  two  processes  are  mutually  corrobo- 
rative. 

This  complement  of  laws  is  assumed  by  Logic  as  its  punctum 
saliens,  and  it  proceeds  to  demonstrate  synthetically  from  them  as 

1  For  the  history  of  these  laws,  see  Hamilton's  Logic,  pp.  62-68. 


10  INTRODUCTORY. 

axioms  the  secondary  or  special  laws  of  the  concept,  the  judgment, 
the  reasoning.  The  whole  of  pure  Logic  is  only  an  articulate  develop- 
ment of  these  Primary  Laws,  and  of  the  various  modes  in  which  they 
are  applied. 

To  say  that  these  self-evident  laws  are  necessary,  is  to  say  that  the 
contradictory  of  each  is  inconceivable.  It  is  not  that  they  are  inviola- 
ble, not  that  the  mind  is  constrained  of  necessity  to  obey  them,  as  a 
planet  is  blindly  constrained  to  obey  the  laws  of  gravitation,  inertia, 
etc.  They  are  violable  in  the  sense  that  we  may  wilfully  or  uncon- 
sciously disregard  them;  but  the  result  is  fallacy,  inconsequence;  or, 
rather,  the  mental  process  is  then  suicidal  or  absolutely  null  and  void. 
All  consequent  thinking  must  be  legitimate ;  i.  e.,  it  necessarily  con- 
forms to  these  laws,  advertently  or  inadvertently.  They  are  the  pri- 
mary conditions  of  the  possibility  of  valid  thought.2 

The  reader  must  not  be  offended  to  find  these  axiomatic  laws  so 
obvious  as  to  seem  mere  truisms.  When  stated,  they  appear  to  have 
been  always  known,  being  implied  in  every  thought  we  have  ever  ex- 
perienced or  observed,  though  until  stated  we  are  as  unconscious  of 
them  as  we  are  of  the  laws  that  govern  our  breathing.  Being  the 
widest  generalities,  penetrating  every  science,  and,  indeed,  governing 
every  mental  movement  that  comprehends  anything,  they  seem  of  all 
things  the  most  familiar  and  trite.  Their  very  truth  requires  that 
they  contain  nothing  new.  Standing  related  to  the  axioms  of  geom- 
etry as  these  are  related  to  elaborate  propositions,  they  at  first  appear 
singularly  meagre,  barren  of  significance,  and  even  frivolous.  But  if 
these  laws  are  really  the  code  by  which  all  human  thought  is  actually 
regulated,  then  their  study  is  not  futile ;  so  far  from  being  barren, 
they  are  the  most  wonderfully  productive  of  principles ;  so  far  from 
being  frivolous,  they  have  the  profoundest  significance. 

§  2.  The  Primary  Laws  of  thought  are  three.  The  first  is  the  Law 
of  Identity.  It  is  the  principle  of  all  logical  affirmation.  It  is  vari- 
ously enunciated:  e.  g.,  Whatever  is,  is,  or  Omne  ens  est  ens ;3  Every- 
thing is  equal  to  itself;*  Every  object  of  thought  is  conceived  as 
itself ; 6  A  thing  is  what  it  is ; 6  Conceptions  which  agree  can  be  united 
in  thought,  or  affirmed  of  the  same  subject  at  the  same  time.7  The 
formula  is  A=A ;  or  A=a'+a"  +  a'" 

3  See  Hamilton's  Logic,  p.  56.      s  Scholastic  form.      4  Hamilton's  Logic,  p.  57 
6  Hansel's  Prolegomena  Logica,  p.  167.  6  Bain's  Logic,  p.  16. 

'Thomson's  Outline,  §  114. 


PRIMARY    LAWS.  11 

The  following  are  examples:  "4  =  4;"  "4=2x2;"  "2  +  2  = 
2X2;"  "4  =  3  +  1,"  etc.;  "According  to  Plato,  The  Idea  is  equal  to 
itself ;"  "  Man's  a  man  for  a'  that ;"  "  Saltpetre  is  nitrate  of  potash  ;" 
"  Francis  Bacon  was  Baron  Verulam ;"  "  Francis  Bacon  was  the  fa- 
ther of  inductive  philosophy  ;"  "  Man  is  rational  and  animal ;"  "  Man 
is  the  last  creation  ;"  "  Man  is  the  only  being  that  laughs ;"  "  A  habit 
is  a  habit ;"  "  What  I  have  written,  I  have  written." 

Hamilton  extends  this  law  to  include  the  relation  of  partial  identity 
or  sameness  in  which  a  concept  stands  to  each  of  its  constituents,  as 
expressed  in  the  second  formula.  E.  g.,  "  Man  is  rational,"  i.  e.  my 
notion  "  Man  "  comprehends  the  notion  "  rational "  as  one  of  its  con- 
stituents ; — similarly,  "  Man  is  animal."  We  may  go  further, — to  the 
part  of  a  part.  E.  g.,  The  notion  animal  comprehends  the  notion  cor- 
poreal, and  we  may  say,  "  Man  is  corporeal."  In  this  extension  of 
the  law,  the  predicate  is  only  a  part  of  what  is  implicated  in  the 
subject. 

To  affirm  that  a  thing  is  itself  seems  to  be  solemn  trifling,  and  is 
ridiculed  by  Locke.  Nulla  propoxitio  est  verier  ilia  in  qua  idem 
prccdicatur  de  seipso.6  When,  however,  we  consider  that  every  ob- 
ject of  thought  has  definite  characteristics  by  which  it  is  marked  off 
and  distinguished  from  all  others  as  being  itself  and  nothing  else,  it 
is  evident  that  every  concept  may  be  viewed  in  relation  to  these  char- 
acteristics, and  that  these  two  several  aspects  must  be  affirmed  of  each 
other.  The  law  then  declares  the  necessity  of  thinking  the  concept 
and  its  constituent  characters  as  the  same.  A  better  expression  of  it 
would  perhaps  be :  A  notion  and  its  constituents  are  the  same.  This 
is  a  more  general  expression  of  the  axiom :  A  whole  is  equal  to  the 
sum  of  its  parts.  In  the  predicate,  the  whole  is  contained  explicitly 
which  in  the  subject  is  contained  implicitly. 

It  is  obvious  that  this  law  enjoins  self-consistency ;  or,  rather,  it  is 
the  necessity  for  self. -consistency  in  thought  that  is  formulated  in 
this  law.  Whatever  be  the  aspects  of  a  thing,  whatever  be  the  modes 
of  statement  concerning  it,  they  must  be  equivalent;  the  thought  un- 
derlying each  must  be  the  same. 

§  3.  The  second  is  the  Law  of  Contradiction.  It  is  the  princi- 
ple of  all  logical  negation.  Enunciations  are:  The  same  attribute 
cannot  be  at  the  same  time  affirmed  and  denied  of  the  same  sub- 

8  Boethius.     See  Hamilton's  Logic,  p.  507. 


12  INTRODUCTORY. 

ject;9  No  subject  can  have  a  predicate  that  contradicts  it;10  \Vhat  is 
contradictory  is  unthinkable  ;  "  No  object  can  be  thought  under  con- 
tradictory attributes  ;  ia  The  same  thing  cannot  be  A  and  non-A  :  this 
room  cannot  be  both  hot  and  cold.13  As  this  law  enjoins  the  absence 
of  contradiction  as  the  indispensable  condition  of  thought,  it  ought 
rather  to  be  called  the  Law  of  Non-contradiction.14  The  formula  is: 
A  is  not  A=0  ;  or,  A  is  not  non-A.  Examples  which,  if  taken  liter- 
ally, violate  the  law  are  :  "  Dotage  is  infancy  in  old  age  ;"  "  His  left 
hand  is  most  dexterous  ;"  "  The  blind  see,  the  deaf  hear,  the  dumb 
speak,"  etc.  ;  "  However  unwilling  the  choice,  he  was  compelled  to 
volunteer  ;"  "  Since  the  war,  all  values  have  risen  ;"  "  Two  kinds  of 
individuals  prepare  extempore  speeches,  fops  and  fools  ;"  "  Nothing 
in  this  life  is  true  ;"  "  The  decomposition  of  the  elements  ;"  "  We 
want  nothing  but  silence,  and  but  little  of  that."  Each  of  the  fore- 
going examples  is  a  logical  paradox,  a  self-contradiction  ;  each  violates 
the  law,  and  is  a  felo  de  se. 

By  a  fundamental  law  of  mind,  which  Bain  calls  the  Law  of  Rela- 
tivity, every  notion  has  an  opposite  or  counter  notion,  and  only  by 
virtue  of  the  one  can  the  other  be  conceived.  To  the  straight  line 
there  is  opposed  the  not-straight  line,  or  crooked  line  ;  to  good  is 
opposed  evil,  and  a  knowledge  of  good  is  impossible  to  a  mind  not 
knowing  evil.  Hence  the  old  scholastic  maxim  :  Contrariorum  eadem 
est  scientia.  Now  these  opposites  cannot  consist,  their  union  is  con- 
tradiction, and  thorough-going  consistency,  as  formulated  in  the  Law 
of  Contradiction,  forbids  it.  Thus,  when  we  affirm  that  this  is  a 
straight  line,  we  must  not  also  say  that  it  is  a  crooked  line  ;  when 
we  think  an  act  good,  we  may  not  also  think  it  evil.  Our  assertions, 
our  thoughts,  to  be  consistent,  must  not  contradict  each  other.  If 
they  do,  the  thought  is  null,  it  destroys  itself.  Having  made  an  as- 
sertion, we  are  to  abide  by  that.  Affirmations  not  self-consistent  are 
unintelligible. 

But  the  principle  of  contradiction  carries  us  one  step  further.  An 
affirmation  being  made,  it  not  merely  forbids  us  to  affirm  also  its  con- 
tradictory, but  it  authorizes  us,  or  requires  us,  to  pronounce  the  con- 
tradictory false  ;  i.  e.,  to  deny,  of  an  object  of  thought,  its  contradic- 

9  Aristotle,  who  says  this  is  by  nature  the  principle  of  all  other  axioms.  —  Metapli. 


10  Kant's  Critique  of  Pare  Reason.     See  Meiklejohn's  transl.  p.  115. 

11  Hamilton's  Logic,  p.  58.  "  Hansel's  Prolegomena  Logica,  p.  167. 

13  Bain's  Logic,  p.  16.  M  Krug's  Logik,  §  18  ;  followed  by  Hamilton. 


PRIMARY    LAWS.  13 

tory.  Accordingly,  the  principle  may  be  enunciated  thus :  Of  two 
contradictories,  one  must  be  false.  E.  g.,  "  This  straight  line  is  not 
crooked ;"  "  This  good  act  is  not  evil ;"  "  No  chastisement  is  joyous ;" 
" Francis  Bacon  was  not  Roger  Bacon;"  "A  dishonest  man  is  not 
trustworthy."  If  all  diamonds  are  precious,  then  to  say  that  some 
or  any  diamonds  are  not  precious  is  false.  Whatever  is  repugnant, 
opposite,  contradictory,  to  a  notion  must  be  denied  of  it. 

The  Laws  of  Identity  and  Contradiction  are  co-ordinate.  Neither 
can  be  deduced  as  a  second  from  the  other  as  first.  In  every  such  at- 
tempt the  evolved  secondary  is  unavoidably  presupposed,  which  is  pe- 
titio  principii.1*  The  two  have,  however,  been  identified  by  many 
eminent  philosophers,  as  Leibnitz,  Wolf,  Kant,  Herbart.  And  Ham- 
ilton says,  "  The  two  laws  are  essentially  one,  differing  only  by  a  pos- 
itive and  negative  form." J  Perhaps  the  two  may  be  fairly  summed 
in  the  statement :  All  thought  must  be  self-consistent. 

§  4.  The  third  is  the  Law  of  Excluded  Middle.  Its  logical  signifi- 
cance is  that  it  limits  the  thinkable  in  relation  to  affirmation ;  for  it 
determines  that  of  the  two  forms  given  in  the  first  two  laws,  the  one 
or  the  other  must  be  affirmed  as  necessary.  No  middle  ground,  no 
third  affirmation,  being  possible,  one  or  the  other  must  be  true. 
Hence  the  names :  Lex  exclusi  medii  aut  tertii  inter  duo  contradicto- 
ria  /  Principium  contradictionis  affirmativum.  Wre  enunciate  it  thus : 
Of  two  contradictories,  one  must  be  true.  Either  a  given  judgment 
must  be  true,  or  its  contradictory :  there  is  no  middle  course.17  Of 
two  contradictories,  one  must  exist  in  every  subject.18  The  formula 
is:  X  is  either  A  or  non-A;  one  being  snblated,  the  other  must  be 
posited. 

A  few  examples  will  suffice :  "  Either  it  is  true  that  God  exists,  or 
it  is  true  that  he  does  not  exist ;"  "  Man  must  be  a  free  agent,  unless 
his  acts  are  necessitated ;"  "  To  be  or  not  to  be,  that  is  the  question ;" 
"  Infinite  mercy  offers  salvation  to  all."  In  this  last  example  the  op- 
position is  between  bounds  and  no-bounds ;  bounds  is  denied  in  "  infi- 
nite," and  hence  no-bounds  must  be  affirmed,  which  is  done  in  "  offers 
salvation  to  all."  The  argument  called  Eeductio  ad  absurdum  is  an 
application  of  this  law.  Of  two  alternatives  it  shows  one  to  be  ab- 
surd, hence  the  other  must  be  true ;  for  one  proposition  being  false, 


15  Shown  in  Hoffbauer's  Logik,  %  23.  16  Logic,  p.  59. 

17  Thomson's  Outline,  §  114.  "  Hansel's  App.  to  Aldrich,  p.  241. 


14  INTRODUCTORY. 

we  are  authorized  or  required  by  this  law  to  pronounce  its  contradic- 
tory true. 

The  Laws  of  Contradiction  and  Excluded  Middle  may  be  conven- 
iently united  in  one  statement,  to  which  might  be  given  the  name 
"  Law  of  Duality."  It  is  the  principle  of  strict  logical  division  and 
disjunction.18  We  may  enunciate  it  thus :  Of  two  contradictories, 
one  must  be  true,  the  other  false ;  Every  predicate  may  be  either  af- 
firmed or  denied  of  every  subject;  Every  assertion  must  be  either 
true  or  false.30  This  compound  form  is  often  mistaken  by  logical 
writers  for  the  Law  of  Excluded  Middle.  So  Goclenius:  Oportet  de 
omni  re  affirmare  aut  negare*1  Hamilton  also.  He  gives  for  the 
Law  of  Excluded  Middle :  Of  contradictory  attributions,  we  can  af- 
firm only  one  of  a  thing ;  and  if  one  be  explicitly  affirmed,  the  other 
is  implicitly  denied."  This  is  the  compound ;  the  latter  member  is 
the  principle  of  contradiction.  His  subsequent  exposition,  however, 
is  correct.  Bain  clearly  makes  the  mistake.23  So  also  Herbert  Spen- 
cer. He  says  the  principle  of  Excluded  Middle  is :  The  appearance 
of  any  positive  mode  of  consciousness  cannot  occur  without  excluding 
a  correlative  negative  mode ;  and  the  negative  mode  cannot  occur 
without  excluding  the  correlative  positive  mode.2* 

§  5.  The  Laws  of  Identity,  Contradiction,  and  Excluded  Middle  arc 
mutually  complementary.  "The  object  which  I  conceive  is  by  the 
Law  of  Identity  discerned  as  being  that  which  it  is,  and  by  the  Law 
of  Contradiction  is  distinguished  from  that  which  it  is  not.  But 
these  two  correlatives  must  also  be  regarded  as  constituting  between 
them  the  universe  of  all  that  is  conceivable ;  for  the  distinction  above 
made  is  not  between  two  definite  objects  of  thought,  but  between  the 
object  of  which  I  think  and  all  those  of  which  I  do  not  think.  Non-A 
implies  the  exclusion  of  A  only,  and  of  nothing  else,  end  thus  denotes 


19  The  'A^ititfia  diaiperiRov  of  the  Greeks. 

20  Mill  questions  the  absolute  truth  of  this  axiom. — Logic,  p.  205.    Tie  says  that 
between  the  true  and  the  false  there  is  a  third  possibility,  the  unmeaning :  e.  g., 
"  Acracadabra  is  a  second  intention,"  is  neither  true  nor  false.     But  is  an  un- 
meaning proposition  any  assertion  at  all  ?     Its  content  is  a  vacuum.     If  unmean- 
ing, it  means  nothing,  says  nothing.     The  third  possibility,  then,  is  nothing ;  or, 
there  is  nothing  between  the  true  and  the  false.     See  also  Examination  of  Ham- 
ilton, ch.  xxi. 

21  Lex.  P/iilosoph.  p.  136.  "  Logic,  p.  59. 

83  Logic,  p.  17.  34  Fortnightly  Review,  No.  5. 


PRIMARY    LAWS.  15 

the  universe  of  all  conceivable  objects  with  that  one  exception."  "  In 
other  words,  A  and  non-A  divide  the  universe  between  them,  admit- 
ting no  intermediate  or  third  possibility,  which  is  declared  by  the  Law 
of  Excluded  Middle. 

By  the  Law  of  Identity,  whatever  is  one  is  that  one. 

By  the  Law  of  Contradiction,  whatever  is  one  is  not  the  other. 

By  that  of  Excluded  Middle,  whatever  is  not  one  is  the  other. 

By  Contradiction,  no  thing  can  be  both  A  and  non-A. 

By  Excluded  Middle,  every  possible  thing  is  either  A  or  non-A. 

By  the  former,  two  contradictories  cannot  both  be  true ;  i.  e.,  one 
must  be  false. 

By  the  latter,  two  contradictories  cannot  both  be  false ;  i.  e.,  ono 
must  be  true. 

Many  fruitless  attempts  have  been  made  to  reduce  the  three  laws 
to  one.  So  intimate  is  their  relation  that  each  supposes  the  other; 
but,  like  the  sides  of  a  triangle,  they  are  not  the  same,  not  reducible 
to  unity,  each  having  equal  right  to  be  considered  first,  and  each,  if 
considered  first,  giving,  in  its  own  existence,  the  existence  of  the  other 
two.  Accordingly  every  attempt  to  deduce  either  one  from  the  others 
has  failed.  They  are  complementary,  co-ordinate,  distinct,  and  insep- 
arable.86 

§  6.  Whatever  violates  either  of  these  laws  we  feel  to  be  impossi- 
ble, not  only  in  thought,  but  in  existence.  We  cannot  believe  that 
anything  can  differ  from  itself,  that  anything  can  at  once  be  and  not 
be,  that  anything  can  neither  be  nor  not  be.  We  cannot  but  regard 
that  as  false  and  unreal  which  these  laws  condemn.  They  thus  de- 
termine to  us  the  sphere  of  impossibility,  and  that  not  merely  in 
thought,  but  in  reality  ;  not  only  logically,  but  metaphysically.  What 
is  contradictory  is  inconceivable  in  thought  and  impossible  in  fact. 

But,  on  the  other  hand,  it  does  not  hold  that  what  is  thought  in 
conformity  with  these  laws  is  therefore  true  in  reality ;  that  whatever 
is  conceivable  in  thought  is  actual,  or  even  possible,  in  fact.  For  the 
sphere  of  thought  is  far  wider  than  the  sphere  of  reality,  and  no  in- 
ference is  valid  from  the  correctest  thinking  of  an  object  to  its  actual 
existence.  What  is  conceivable  conforms  to  the  laws  of  thought,  and 

88  Mansel's  Prolegomena  Logica,  p.  168.       39  Hamilton's  Logic,  pp.  70  and  506. 


16  INTRODUCTORY. 

is  said  to  be  logically  possible,  i.  e.,  possible  in  thought ;  and  this  is 
true  of  many  things  that  are  impossible  in  fact.  Pure  mathematics 
deals  exclusively  with  mere  logical  possibilities.  That  the  stars  may 
fall  on  the  earth  is  physically  impossible ;  that  revenge  may  be  a 
duty  is  ethically  impossible.  But  both  are  conceivable ;  they  may  be 
represented  in  thought;  they  are  logically  possible.  I  may  think 
Waterloo  a  fiction,  or  Christianity  a  failure,  but  this  conceivability  is 
no  evidence  that  they  are  so.  While,  then,  these  laws  are  the  high- 
est criterion  of  the  non-reality  of  an  object,  they  are  no  criterion  at 
all  of  its  reality ;  and  they  thus  stand  to  existence  in  a  negative,  and 
not  in  a  positive,  relation.  Says  Kant,  "  The  principle  of  contradic- 
tion is  a  universal  but  purely  negative  criterion  of  all  truth."  "  And 
this  holds  equally  of  all  the  proximate  and  special  applications  of 
these  laws ;  that  is,  of  the  whole  of  Logic.  Our  science,  then,  in  its 
relation  to  other  sciences,  is  not  a  positive  criterion  of  truth ;  it  can 
only  be  a  negative  criterion,  being  conversant  with  thoughts  and  not 
with  things,  with  the  possibility  and  not  the  reality  of  existence. 

We  have  referred  to  the  psychological  Law  of  Relativity.  Some 
eminent  German  philosophers  have  held  that  the  human  mind  is 
competent  to  the  cognition  of  the  absolute,  or  that  which  has  no  rela- 
tion, and  have  elaborated  thereon  extensive  systems  of  philosophy. 
This  Philosophy  of  the  Absolute  can  proceed  only  upon  a  more  or 
less  complete  denial  of  the  primary  laws  of  thought.  Fichte  and 
Schelling  admit  the  Law  of  Identity,  but  deny  the  two  others,  "  the 
empirical  antagonism  between  the  Ego  and  the  Non-ego  being  merged 
in  the  identity  of  the  absolute  Ego."  Hegel  regards  all  the  laws  as 
valid,  but  only  for  the  finite  Understanding,  they  being  inapplicable 
to  the  higher  processes  of  the  Reason.  The  eclecticism  of  Cousin  at- 
tempts the  cognition  of  the  absolute  without  repudiating  the  laws  of 
Logic.  It  is  therefore  at  once  involved  in  undeniable  contradictions 
from  which  there  is  no  escape. 

§  7.  The  principle  of  Sufficient  Reason,  or  Determinant  Reason, 
has  been  laid  down  as  a  fourth  primary  law  of  thought.  It  is  enun- 
ciated thus :  Every  judgment  must  have  a  sufficient  ground  for  its  as- 
sertion. It  was  first  distinctly  enounced  by  Leibnitz,  who  made  it, 
together  with  the  principles  of  Identity  and  Contradiction,  the  basis 
of  his  Logic.  Kant  adopted  it,  regarding  Contradiction  as  the  crite- 

87  Critique  of  Pure  Reason,  p.  115. 


PRIMARY    LAWS.  17 

rion  of  logical  possibility,  and  Sufficient  Reason  as  the  criterion  of 
logical  reality.  But  logical  possibility  and  logical  reality  are  one. 
Hamilton,  in  his  lectures,  followed  Fries  and  Krug  in  admitting  the 
principle  to  this  high  position  in  Logic,  but  subsequently  he  gave 
it  up,  and  pronounced  it  extralogical."  Mansel  says,  "  The  relation 
of  this  principle  to  the  act  of  judgment  is  merely  negative ;  it  forbids 
us  in  certain  cases  to  judge  at  all,  and  it  does  no  more.  .  .  .  The  only 
logical  reason  for  a  thought  of  any  kind  is  its  relation  to  some  other 
thought ;  and  this  relation  will  in  each  case  be  determined  by  its 
own  proper  law,"  i.  c.,  by  one  or  more  of  the  three  given  Primary  Laws. 
"The  principle  of  Sufficient  Reason  is  therefore  no  law  of  thought,  but 
only  the  statement  that  every  act  of  thought  must  be  governed  by 
some  law  or  other." 2  Adopting  this  view,  we  reject  the  principle, 
as  forming  no  positive  element  of  Logic.  N 

§  8.  In  connection  with  the  Primary  Laws,  it  is  appropriate  to 
state  an  important  Postulate  of  Logic.  It  is  this :  Logic  postulates 
to  be  allowed  to  state  explicitly  in  language  all  that  is  implicitly  con- 
tained in  the  thought.90  According  to  Aristotle,  the  doctrine  of  the 
syllogism  deals,  not  with  the  expression  of  reasoning  in  ordinary  lan- 
guage, but  with  the  internal  reasoning  of  the  mind  itself.  Logic, 
therefore,  has  always  presented  all  the  propositions  of  a  syllogism,  al- 
though in  actual  argument  one  or  more  of  them  is  usually  left  unex- 
pressed. But,  since  all  speech  is  very  elliptical  and  highly  rhetorical, 
the  postulate  must  be  allowed  to  Logic  in  general,  and  must  be  fur- 
ther extended  to  include  not  only  the  accurate  and  complete  rendition 
of  the  thought  into  language,  however  prolix  and  awkward  its  expres- 
sion may  be,  for  Logic  disregards  rhetorical  elegance,  but  also  the 
transmuting  of  metaphors,  and,  indeed,  of  all  rhetorical  forms,  into  the 
most  literal  and  direct  statement  practicable,  providing  only  that  the 
thought  itself  be  not  changed.  For  as  Logic  deals  only  with  the 
thought,  it  must  be  independent  of  the  accidents  of  expression. 

Hence  when  a  logician  deals  with  an  abbreviated  or  figurative  ex- 
pression, one  wherein  "  more  is  meant  than  meets  the  ear,"  for  much 
thought  is  conveyed  in  hints,  intimations,  and  metaphors,  he  at  once 
asks,  What  is  the  full  and  true  meaning  of  this?  He  then  proceeds, 
and  must  be  allowed  to  strip  off  all  ornament,  to  supply  all  Iacuna3, 

38  Logic,  p.  62,  note  ;  and  p.  251.  29  Prolegomena  Logica,  p.  182. 

30  Hamilton's  Logic,  p.  81. 


18  INTRODUCTORY. 

and  to  exhibit  the  thought  naked  and  entire.  This  is  often  difficult 
to  do,  thought  being  so  subtle  and  evasive,  and  language  so  meagre 
and  inaccurate.  He  must  be  allowed,  too,  to  make  changes  in  phra- 
seology for  mere  convenience,  provided  always  the  thought  is  not 
thereby  essentially  modified.  Such  alternative  and  entirely  similar 
propositions,  having  equal  power  and  reach,  are  called  "  Equipollent 
Propositions,"  a  term  for  which  we  shall  have  much  use  in  the  se- 
quel. Mill  states  the  matter  thus :  "  Logic  postulates  to  be  allowed 
to  assert  the  same  meaning  in  any  words  which  will  express  it;  we 
require  the  liberty  of  exchanging  a  proposition  for  any  other  that  is 
equipollent  with  it."  The  justice  of  the  Postulate  is  self-evident  on 
the  ground  that  Logic  deals  not  with  words,  but  with  thoughts. 


PAET  SECOND.— OF  CONCEPTS. 


I.  THE   TERM. 

§  1.  Thought  viewed  as  a  product  of  intellect  exhibits  three  forms, 
the  Concept,  the  Judgment,  the  Reasoning,  which,  when  expressed  in 
language,  severally  appear  as  the  Term,  the  Proposition,  the  Syllo- 
gism. The  three  are  not  different  in  kind,  for  both  concepts  and  rea- 
sonings may  be  reduced  to  judgments.  A  concept  is  the  result  of  one 
or  more  prior  acts  of  judgment',  and  may  be  analyzed  into  these  again. 
A  reasoning  is  a  judgment  of  the  relation  of  two  things  through 
their  relations  to  a  third.  But  each  of  these  forms  of  thought  calls 
for  distinct  consideration,  and  constitutes  a  general  division  of  ele- 
mentary Logic.  Under  Concepts,  then,  let  us  consider  first  their 
Origin,  they  and  their  constituent  elements  being  comprised  by  the 
common  title  of  the  N6tion,  or  the  Term. 

§  2.  An  account  of  the  genesis  of  concepts  belongs  more  strictly  to 
Psychology,  but  cannot  be  entirely  omitted  here.  Three  momenta 
may  be  distinguished,  viz.,  Abstraction,  Generalization,  Conception. 
First  of  Abstraction. 

When  the  mind  is  attracted  to  some  object,  either  an  external  thing 
as  presented  in  sense,  or  a  mental  image  presented  in  memory,  it  ap- 
prehends it  only  as  possessed  of  a  number  of  qualities.  These  qual- 
ities are  apprehended  as  unlike  each  other  and  several,  the  mind  ex- 
periencing what  is  called  "  the  shock  of  difference."  If  attention  is 
now  fixed  on  one  quality,  as  the  color,  or  the  weight,  then  while  the 
other  qualities  consequently  become  obscure,  or  perhaps  pass  out  of 
consciousness,  this  one  on  which  attention  is  fixed  is  thereby  drawn 
into  vivid  consciousness,  becoming  the  chief,  if  not  the  exclusive,  ob- 
ject of  cognition.  Thus  by  attention  to  this  one  quality  the  mind 
has  been  abstracted  or  drawn  away  from  all  others.  In  this  psycho- 
logical view  Abstraction  is  the  negative  correlative  of  the  positive  act 


20  OF    CONCEPTS. 

of  attention,  the  mind  being  denied  to  a  plurality  of  qualities,  in  being 
concentrated  on  one.  But  this  one  quality  may  be  considered  as 
abstracted  or  drawn  away  from  all  others.  In  this  logical  view  Ab- 
straction is  a  positive  act  by  which  we  cognize  one  quality  apart.  It 
is  thus  by  abstraction  that  we  obtain  a  clear  and  distinct  notion  of 
the  qualities,  attributes,  properties,  characters,  features,  etc.,  of  an  ob- 
ject, all  of  which  terms  are  nearly  synonymous,  and  are  included  in 
Logic  under  the  one  term,  marks. 

It  may  be  at  once  noted  that  marks  are  of  several  sorts  or  kinds. 
They  are, — 

1st.  Positive  or  negative;  as  rational  is  a  positive,  and  imperfect 
a  negative,  mark  of  man. 

2d.  Essential,  necessary,  or  accidental,  contingent ;  as  rational  is  an 
essential,  and  learned  an  accidental,  mark  of  man. 

3d.  Original  or  derivative ;  as  rational  is  an  original,  calculating  a 
derivative,  mark  of  man,  this  being  a  consequence  of  his  rationality. 

4th.  Simple  or  complex ;  as  conscious  is  a  simple  mark  (i.  e.,  one 
not  susceptible  of  analysis)  and  animal  a  complex  mark  of  man,  the 
latter  being  compounded  of  organized  and  sentient.  So  red  is  a  simple 
mark  of  one  kind  of  rose,  and  vegetable  a  complex  mark. 

5th.  Common  or  peculiar;  as  mortal  is  a  mark  common  to  man 
with  other  animals,  risible  a  peculiar  mark,  found  in  no  other  being. 
A  peculiar  mark  is  called  "  a  property,"  as  belonging  to  this,  and  to 
no  other,  yet  not  considered  essential ;  thus  mobile  is  a  property  of 
body.  A  particular  mark  is  one  belonging  to  a  single  individual 
alone ;  as  the  mark  set  upon  Cain. 

The  number  of  marks  which  may  be  discerned  in  any  object  is  in- 
definitely great.  It  would  be  impossible  to  enumerate  exhaustively 
all  the  marks  which  might  be  discerned  in  so  simple  an  object  as  a 
grain  of  corn. 

§  3.  But  objects  are  presented  to  us  in  sense  or  in  memory  as  many 
and  complex.  In  our  apprehending  them,  very  many  of  their  marks 
produce  the  shock  of  difference,  or  produce  dissimilar  impressions; 
but  some  givk  the  shock  of  similarity,  or  produce  similar  impressions. 
The  repetition  of  an  impression  is  precisely  what  excites  attention,  or 
determines  the  direction  of  reflective  consciousness.  When  some  ob- 
jects are  found  to  agree  in  certain  respects,  while  others  wholly  dis- 
agree, consciousness  is  concentrated  naturally  on  those  which  partially 
agree ;  and  then,  in  them,  on  those  marks  in  or  through  which  they 


THE    TERM.  21 

agree.  So  far  this  is  mere  abstraction.  To  give  a  crude  illustration : 
We  observe  a  number  of  animals;  our  attention  is  attracted  to  a 
horse,  an  ox,  a  goat,  a  dog,  etc.,  differing  greatly  from  the  birds,  pep-- 
tiles, etc.,  that  may  be  present,  but  agreeing  in  some  respects.  We 
then  observe  more  particularly  that  each  has  a  hairy  hide,  and  is/otwv 
footed,  in  which  marks  they  agree. 

Similar  marks  are  those  which  stand  in  similar  relation  to  our  or- 
gans and  faculties  of  cognition.  When  the  similarity  is  complete, 
the  effects  which  they  produce  in  us  are  indiscernible.  But  what  we 
cannot  distinguish  is  to  us  virtually  the  same ;  i.  e.,  they  are  subjective- 
ly to  us  identical,  as  if  they  were  objectively  identical.  The  same, 
accordingly,  we  consider  them  to  be,  though  really  in  different  ob- 
jects. This  act,  to  think  the  similar  the  same,  is  the  essence  of  all 
Generalization ;  so  we  may  say  that  to  generalize  is  to  think  the  sim- 
ilar the  same.  It  is  a  fiction  of  thought,1  but  one  without  which  our 
limited  powers  would  be- unable  to  grasp  the  multiplicity  of  objects 
presented  to  us.  We  think  that  each  of  the  animals  named  in  the 
above  example  has  the  same  mark,  e.  g.,  four-footed.  This  mark  is 
now  applicable  to  either  of  the  objects.  A  plurality  has  been  reduced 
to  unity  in  thought.  Such  a  generalized  mark  is  a  simple  general  ab- 
stract notion. 

We  may  observe  by  anticipation  that  generalization  is  classification. 
They  are  but  different  aspects  of  the  same  operation.  By  thinking  a 
mark  as  common  to  several  individuals,  we  thereby  group  them,  we 
constitute  a  class  containing  them.  Thus  the  animals  above  named 
belong  to  the  class  or  group  quadruped. 

Also  we  remark  that  when  we  speak  of  observing  a  number  of  an- 
imals together,  we  have  already  thought  them  as  one  group.  Their 
common  marks  have  already  been  generalized,  and  thereby  we  have 
already  constituted  the  total  of  the  objects  considered  into  the  class 
animal. 

Now  let  it  be  noted  that,  having  affirmed  the  mark  four-footed  of 
some  of  these  objects,  thereby  constituting  a  class,  we,  in  the  same 
act,  under  the  shock  of  dissimilarity,  deny  this  mark  of  the  rest.  The 
birds,  reptiles,  etc.,  are  thereby  constituted  into  a  negative  class;  i.  e., 

1  Overlooking  the  fictitious  character  of  this  act,  and  thinking  the  similar  to  be 
really  the  same,  gave  rise  to  the  erroneous  doctrine  of  the  Realists  of  mediaeval 
times,  that  a  universal  objectively  exists  independently  of  things,  and  is  common 
to  all  things  of  one  kind.  See  Whately's  chapter  on  Realism,  Logic,  p.  305  sq. ; 
Thomson's  Outline,  §  62 ;  and  Ucberweg's  History  of  Philosophy,  §  91  sq. 


22  OF    CONCEPTS. 

one  characterized  by  the  negative  mark,  non-four-footed.  These  two 
groups  are  dissimilar  in  that  one  possesses  the  mark  four-footed,  and 
the  other  does  not.  The  sum  of  the  two  groups,  the  A  and  non-A, 
equals  the  total  of  the  universe,  animal.  Further,  if  we  contemplate 
the  special  group  quadruped,  we  again  experience  the  shock  of  similar- 
ity and  of  dissimilarity.  The  ox  and  the  goat  each  have  horns ;  being- 
similar,  we  generalize  and  call  them  horned  quadrupeds.  The  horso 
and  the  dog  have  no  horns ;  being  similar  in  this  negative  respect, 
we  generalize  them  into  a  negative  group  of  non -horned  quadrupeds. 
But,  at  the  same  time,  the  two  groups  being  dissimilar  in  respect  of 
having  and  not  having  horns,  we  think  them  different  or  diverse. 
They  are  thus  specialized,  or  classified  into  two  co-ordinate  kinds,  the 
horned  and  the  non -horned,  subordinate  to  quadruped,  which  is  their 
sum.  This,  then,  is  Specialization,  the  necessary  correlative  to  gen- 
eralization, and  we  may  say  that  to  specialize  is  to  think  the  dissim- 
ilar diverse,  or  different,  or  distinct.  It  also  is  classification.  It  is 
not  a  process  distinct  from  generalization,  for  neither  occurs  without 
the  other;  they  mutually  imply  each  other. 

§  4.  The  third  moment  of  thought  is  Conception,  its  product  the 
Concept.  To  conceive  (con-capere)  is  to  grasp  together.3  When  a 
number  of  marks  have  been  abstracted,  they  may  be  collected  by 
thought  into  one  notion,  and  this  referred  to  substance  constitutes  a 
concept.  A  concept,  then,  is  a  union  of  marks  in  one  notion ;  or,  a 
concept  is  a  bundle  of  marks  thought  of  as  inhering  in  some  thing. 

Every  thing  presented  to  the  mind  has  an  indefinite  plurality  of 
marks.  Observation  can  make  many  known  to  us,  but  our  knowl- 
edge, though  constantly  increasing  in  fulness  and  complexity,  can 
never  exhaust  them.  Moreover,  the  limited  powers  of  the  mind  can- 
not take  in  at  once  all  those  marks  whose  presence  is  known.  A 
representation  becomes  confused  when  we  attempt  to  grasp  or  com- 
prehend in  one  more  than  a  very  few  of  them.  Giving  up  the  at- 
tempt, we  form  a  concept  of  the  thing,  embracing  comparatively  few 
of  its  ascertained  marks,  making  a  selection  of  those  which  are  most 
distinctive  and  essential.  The  concept  or  notion,  therefore,  involves 
the  representation  of  a  part  only  of  the  marks  of  which  an  individual 
object  is  the  sum,  and  consequently  affords  only  a  one-sided  and  in- 

3  So  the  German  begrafm,  cognate  to  our  words  "  grip,"  "  grab,1'  "  group,"  etc. 
Hence  Begriff\&  the  German  for  "concept." 


«B8ITX 


- 

THE    TERM.  23 

adequate  knowledge  of  the  thing.  This  inadequacy  of  concepts  is 
a  further  consequence  of  the  limited  powers  of  mind,  which  must  ac- 
cept a  small  part  as  though  it  were  the  whole  of  a  thing. 

For  example,  I  take  the  marks,  citizen  of  Athens,  teacher  of  I^a/to, 
son  of  Sophroniscus,  husband  of  Xantippe,  famous,  virtuous,  inquis- 
itive, moralist,  martyr  of  philosophy, — these  and  perhaps  others, — 
and  constitute  my  notion  of  Socrates.  I  may  know  much  more  about 
him,  but  practically  this,  or  some  such  limited  group  of  marks,  com- 
prises all  that  I  use  in  representing  him. 

"  Every  object,"  says  Drobisch,  "  is  thought  as  a  determinate  ob- 
ject only  through  the  marks  appertaining  to  it,  by  means  of  which 
it  is  comparable,  in  respect  to  its  nature,  with  other  things,  and  is 
distinguishable  from  them.  Without  these  marks  it  is  only  an  inde- 
terminate something,  a  thing  or  being  without  further  determination. 
These  marks,  on  the  other  hand,  have  no  independent  being  in  and 
for  themselves,  but  can  be  separated  only  in  thought  from  the  object 
in  which  they  exist.  In  the  concept  of  the  object,  then,  there  is  the 
thought  of  an  independent  but  indeterminate  something  united  with 
determinate  but  dependent  marks.  The  concept  of  the  object  is  the 
union  of  the  two." 

In  the  concept  as  now  described  we  may  consider  that  the  consti- 
tuting marks  are  not  generalized.  A  notion  of  this  sort  is  complex, 
but  not  general.  We  may  say  that  such  is  the  concept  of  an  individ- 
ual, and  to  this  form  of  concept  Esser's  definition  applies :  A  con- 
cept is  the  representation  of  a  thing  through  its  distinctive  marks. 
It  should  be  observed,  however,  that  such  a  concept  of  an  individual 
is  potentially  general,  potentially  a  class  notion.  Thus  there  might  be 
several  persons  having  all  the  marks  attributed  above  to  Socrates, 
and  forming  my  notion  of  him.  Should  it  be  found  so,  I  must  seek 
and  add  to  my  concept  some  particular  mark,  and  thus  secure  the  sin- 
gular character  of  my  concept.  Hence  every  concept  of  an  individual 
should  comprise  at  least  one  particular  mark  by  which  it  is  distin- 
guished from  all  other  things. 

When  a  concept  is  constituted  of  common  marks,  marks  which 
have  been  generalized,  the  notion  is  then  complex  and  general,  and 
contains  under  it  the  several  things  to  which  the  marks  are  common ; 
i.  e.,  it  is  a  class  notion.  For  example,  I  take  the  following  various 
marks,  which  I  have  abstracted  and  generalized,  which  I  have  thought 
of  as  common  to  a  number  of  individual  things :  self-luminous, 
bright,  sparkling,  celestial,  very  distant,  relatively  fixed,  etc. ;  and, 


24  OF    CONCEPTS. 

making  a  unity  of  this  plurality,  I  form  my  concept  of  star.  This 
complex  notion  is  applicable  to,  or  contains  under  it,  a  host  of  distinct 
things,  for  each  of  many  individuals  has  all  these  marks.  The  notion 
is  therefore  general,  and  the  word  "  star,"  which  has  been  adopted  to 
stand  for  or  express  this  bundle  of  marks,  is  the  common  name  of 
many  individuals.  To  this  form  of  concept  Hansel's  definition  ap- 
plies: A  concept  is  a  combination  or  reduction  to  unity  in  thought 
of  the  similar  qualities  or  marks  of  the  objects  thought  upon,  which 
are  thereby  constituted  into  a  class. 

We  may  now  more  adequately  define  thought  as  the  act  in  which 
the  mind  knows  things  by  means  of  concepts.  To  think  is  to  con- 
ceive,— is  to  form  concepts. 

§  5.  It  is  obvious  that  the  concept  expresses  merely  the  relation 
of  similarity  between  the  things  it  denotes,  implying,  of  course,  that 
there  are  also  differences.  But  a  mere  relation  cannot  be  realized  in 
consciousness;  for  to  suppose  wre  can  cognize  a  relation  of  things, 
and  yet  not  the  things  related,  is  contradictory  and  absurd.  Or,  an 
act  of  cognition  necessarily  implies  an  object  cognized ;  but  a  relation 
stripped  of  its  terms  cannot  be  an  object,  since  there  is  nothing  in  it 
opposite  to  the  thinking  subject.  A  concept,  therefore,  is  not  cogniz- 
able in  itself;  that  is,  it  affords  no  absolute  or  irrespective  object  of 
knowledge.  A  concept  can  be  realized  in  consciousness  only  by  ap- 
plying it  to  one  or  more  of  the  objects  related  as  similar  in  those  re- 
spects. When  we  attempt  to  represent  by  an  image  any  abstract 
generality  as  an  absolute  object,  we  find  it  impossible.  We  can  thus 
realize  it  only  as  attached  to  some  individual  and  determinate  object. 
Its  whole  generality  is  found  to  consist  in  this :  that  though  we  must 
realize  it  in  thought  as  comprised  in  some  individual  of  the  class,  we 
may  do  it  under  any.  The  generality  of  a  concept,  then,  is  potential, 
not  actual.2 

For  example :  I  have  the  general  notion  triangle,  a  figure  of  three 
sides.  This  term  is  applicable  to  several  species,  among  others  to 
the  equilateral  and  to  the  scalene.  Now  should  I  attempt  to  realize 
triangle  in  its  generality,  it  must  be  at  the  same  time  both  equilateral 
and  scalene.  But  herein  is  a  contradiction ;  the  image  must  have  its 
sides  all  equal  and  yet  unequal.  Hence  such  an  image  is  impossible. 
Still,  while  the  image  cannot  be  both  equilateral  and  scalene,  it  must 

a  See  Hamilton's  Logic,  pp.  91,  96. 


THE    TERM.  25 

be  one  or  the  other.  I  image,  then,  or  else  draw  with  my  pencil,  an 
equilateral  triangle ;  and  by  disregarding  the  equality  of  its  sides,  and 
all  particular  marks  characterizing  this  individual  figure,  I  can  con- 
template alone  the  notion  trilateral  figure  which  it  comprises.  Thus 
only  is  the  concept  triangle  realized  in  consciousness. 

§  6.  It  must  not  be  understood  that  the  three  momenta  now  de- 
scribed are  actually  separate  and  successive  in  the  mind.  They  are 
not  in  reality  distinct  and  independent  acts,  but  are  only  so  distin- 
guished and  stated  in  order  to  enable  us  to  comprehend  and  speak  of 
the  several  aspects  of  an  actually  indivisible  operation.  It  is  merely 
a  logical  analysis.  For  instance,  the  generalization  of  a  mark  cannot 
occur  without  a  classification ;  that  is,  without  a  grouping  of  several 
objects  in  one  class,  which  is  essentially  conception ;  and,  again,  ab- 
straction is  analysis,  which  implies  that  there  was  already  by  the  mind 
a  synthesis,  though  it  may  have  been  very  obscure,  of  marks,  from 
among  which  one  is  drawn  into  clear  consciousness;  but. a  synthesis 
of  marks,  however  obscure,  is  conception. 

Moreover,  a  mark  and  a  concept  are  commutable.  Every  mark  is 
potentially  a  concept,  and  every  concept  potentially  a  mark.  A  con- 
cept is  expressed  by  a  substantive  or  substantive  phrase ;  a  mark  by 
an  adjective  or  adjective  phrase ;  and  the  transmutation  of  these 
grammatical  forms,  corresponding  to  the  change  in  the  aspect  of 
thought,  is  a  familiar  fact.  Thus  :  "  Man  is  an  animal,  or  is  animal." 
Here  animal  is  used  first  as  a  concept,  next  as  a  mark.  The  distinc- 
tion consists  in  the  use  made  of  the  notion  by  thought.  If  used  de- 
notatively, the  notion  is  a  concept ;  if  used  connotatively,  the  notion 
is  a  mark.  Thus :  "  Man  is  an  animal "  means  that  man  is  one  of  the 
kinds  of  things  denoted  by  the  class  animal ;  but  "  Man*  is  animal r' 
means  that  man  has  the  attributes  connoted  by  the  mark  animal. 

Let  it  be  now  observed  that  here,  and  throughout  this  treatise,  the 
word  "  notion "  is  used  genetically ;  it  means  either  a  concept  or  a 
mark.  The  two  are  so  freely  convertible,  so  constantly  changing  the 
one  into  the  other  in  thought,  that  we  need  a  common  term  to  ex- 
press either.  For  this  the  word  "  notion  "  is  most  suitable. 

§  7.  In  this  connection  may  be  noticed  another  very  subtile  but 
very  common  play  of  thought.  A  mark,  which  is  strictly  only  the 
quality  or  attribute  of  something,  is,  this  relation  being  obscured  by 
abstraction,  often  thought  of  as  though  it  were  itself  a  thing.  In- 


26  OF    CONCEPTS. 

stead  of  being  referred  to  its  original  substance,  it  is,  as  it  were,  com- 
pletely severed  therefrom  by  thought,  and  established  in  an  indepen- 
dent existence.  Marks  so  treated  are  specifically  called  "  abstractions," 
and  are  expressed  by  abstract  terms,  of  which  a  great  number  have 
the  termination  "-ness."  Thus:  blue  is  a  mark  of  the  sky,  of  the 
ocean,  of  sapphire,  etc. ;  but  fineness  is  thought  of  as  something  inde- 
pendent of  these  things,  and  spoken  of  as  though  it  had  a  real  exist- 
ence by  itself.  Again,  Aristides  is  just,  but  justice  is  extolled  apart 
from  any  person.  In  the  one  case  the  mark  is  thought  as  concrete 
(con-crescere=to  grow  together),  as  inherent  in  something;  in  the 
other  case  it  is  thought  as  entirely  abstract.  These  are  proper  oppo- 
sites.  Human  is  concrete ;  humanity,  abstract.  A  concrete  term  is 
the  name  of  an  object;  an  abstract  term  the  name  of  an  attribute. 
An  abstract  term,  then,  is  the  name  of  a  mark  thought  as  a  thing.3 

The  uncounted  multitude  of  sucli  terms  in  every  refined  language 
shows  what  familiar  use  is  made  by  human  thought  of  this  fiction. 
The  concrete  and  the  abstract  are  different  regions  of  thought,  and 
the  difference  should  be  clearly  and  constantly  observed,  as  a  confus- 
ing of  one  with  the  other  often  leads  to  the  grossest  absurdities. 
Plato,  in  the  Sopkistet,  not  recognizing  the  factitious  and  fictitious 
nature  of  abstracts,  argues  that  things  may  exist  which  are  incorpo- 
real; for  justice  and  wisdom,  says  he,  are  incorporeal;  and  justice 
and  wisdom  must  be  something.  By  "  something  "  he  means  a  thing 
capable  of  existing  in  and  by  itself,  and  not  merely  as  the  quality  of 
some  other  thing.  From  this  source  grew  the  Platonic  doctrine  of 
Ideas,  teaching  that  abstracts  are  independent  entities.  The  Aristote- 
lian doctrine  of  substantial  forms  and  second  substances,  and  all  the 
idle  speculations  respecting  TO  ov,  TO  eV,  TO  vpotot',  and  similar  ab- 
stractions, have  the  same  origin.  Many  of  the  gross  blunders  of 
modern  metaphysics  are  attributable  to  this  confusion  of  the  abstract 
and  concrete.  "  If  the  student  of  philosophy  would  always,  or  at  least 
in  cases  of  importance,  adopt  the  rule  of  throwing  the  abstract  lan- 
guage in  which  it  is  so  frequently  couched  into  a  concrete  form, 
he  would  find  it  a  powerful  aid  in  dealing  with  the  obscurities  and 
perplexities  of  metaphysical  speculation.  He  would  then  see  clearly 
the  character  of  the  immense  mass  of  nothings  which  constitute  what 
passes  for  philosophy." 4 

•  See  Mill's  Logic,  bk  i,  ch,  ii,  §  4. 

4  Bailey's  Letters  on  tiic  Mind,  vol.  ii,  p.  139,    See  remarks  of  Bain,  Logic,  p.  52  sq. 


THE    TERM.  27 

§  8.  It  is  important  to  consider  the  relation  of  language  to  our  con- 
cepts. A  concept  would  immediately  fall  back  into  the  infinitude 
and  confusion  from  which  it  has  been  called  out  were  there  not  some~ 
means  by  which  to  render  it  permanent.  This  is  accomplished  by 
words.  The  concept  is  fixed  and  ratified  in  a  verbal  sign,  by  means 
of  which  it  can  at  any  time  be  recalled  into  consciousness.  Lan- 
guage, then,  is  the  attribution  of  signs  to  our  cognitions  of  things. 
It  is  the  register  of  thought.  Many  thoughts  are  valuable  either  not 
at  all  or  only  for  the  moment,  and  are  dismissed.  Any  one  of  high 
value  and  needed  for  further  use  is  preserved  by  a  sign ;  we  give  it  a 
name.  "  Nomina  sunt  notionum  notce." 

The  name  of  a  general  notion  is  a  common  noun.  Every  common 
noun,  therefore,  expresses  a  fasciculus  of  attributes  belonging  to  each 
of  several  objects.  It  stands  for  a  product  of  thought,  and  is  a  fac- 
titious unit  to  be  used  in  further  thought.  We  have  already  re- 
marked that  a  concept  is  expressed  by  a  substantive  noun,  a  mark  by 
an  adjective  noun,  and  that  an  abstract  noun  is  the  name  of  a  mark 
considered  as  a  thing.  We  may  add  that  a  verb  is  the  name  of  an 
action,6  and  also  that  many  notions  are  registered  in  phrases  instead 
of  single  words ;  e.  g.,  we  have  no  single  word  to  express  our  notion 
of  "  a  rainy  day."  A  singular  noun  applies  to  only  one  object,  like 
a  proper  name,  but  then  it  is  singular  only  in  its  present  application ; 
as  "a  song,"  "this  world,"  "my  horse,"  "the  king."  It  is  evident 
that  the  singular  meaning  is  obtained  by  adding  some  limiting  word. 
The  indefinite  article  means  "  some  or  any  one  of  the  class ;"  as  in 
"  Give  us  a  song."  The  definite  article,  together  with  demonstratives, 
possessives,  etc..  indicates  a  particular  individual,  yet  designates  it  as 
belonging  to  a  class ;  as  "  The  king  comes,"  "  Cesar's  army."  All 
such  names  are  connotative,  they  imply  attributes  or  marks,  and  when 
used  to  denominate  a  subject  they  carry  these  marks  into  the  subject 
and  attribute  them  to  it.  A  proper  name  strictly  is  non-connotative.6 
It  denotes  an  individual,  but  does  not  indicate  or  imply  any  attributes 
of  that  individual.  It  is  not  the  name  of  a  quality  or  qualities ;  it 
is  but  an  unmeaning  mark  or  sign  which  we  connect  in  our  minds 
with  an  object,  so  that  when  this  sign  meets  our  eyes  or  ears  we  may 

6  J.  C.  Scaliger  traced  the  distinction  between  the  noun  and  the  verb  to  a  differ- 
ence of  time ;  for  the  noun  represents  a  permanent  thing,  the  verb  a  temporary 
and  transitory  state. 

6  See  Mill's  Logic,  bk.  i,  ch.  ii,  §  5,  for  an  able  discussion  of  the  distinction  be- 
tween connotative  and  non-connotative  terms. 


28  OF    CONCEPTS. 

think  of  that  individual ;  it  does  not  of  itself  connote  or  imply  any 
quality  of  the  individual,  nor  convey  any  information  respecting  it. 
This  is  true  of  the  proper  name  considered  as  the  name  or  sign  of  an 
individual  object  presented  to  mere  intuition.  But  if  it  stands  for  or 
expresses  my  notion  of  an  individual,  it  is  evidently  a  complement  of 
marks,  and  connotes  an  indefinite  plurality,  as  in  the  example  given 
above  (§  4)  of  the  notion  Socrates.  When  Euclides,  having  heard  of 
the  fame  of  Socrates,  went  from  Megara  to  Athens  to  see  him,  and 
some  one  pointed  him  out,  saying,  That  person  is  Socrates,  then  cer- 
tainly the  proper  name,  thus  attributed  to  the  person,  connoted  and 
carried  with  it  the  marks  which  constituted  Euclides'  notion  of  Soc- 
rates, and  identified  this  concept  with  that  person. 

While  language  is  not  absolutely  necessary  to  thought,  for  the 
thought  must  have  been  prior  to  its  name,  it  is  necessary  to  any  con- 
siderable progress.  Without  it  we  could  never  rise  above  the  very 
lowest  degrees  in  the  scale  of  thought.  A  sign  is  necessary  to  give 
stability  to  our  intellectual  progress,  to  establish  each  step  in  advance 
as  a  new  starting-point  for  our  advance,  to  another  beyond.  Without 
language  there  could  be  no  knowledge  realized  of  the  essential  proper- 
ties of  things,  and  all  ascent  from  the  sphere  of  sense  to  the  sphere  of 
moral  and  religious  intelligence  is  without  it  impossible,  or  possible 
only  to  a  very  low  degree.7 

In  thinking  without  language,  it  follows  from  what  was  said  in  §  5 
that  at  every  step  in  the  process  each  motion  must  be  realized  in  con- 
sciousness by  the  image  of  an  example.  It  is  obvious  that  this  is  a 
clumsy  and  very  restricted  procedure.  By  the  device  of  language  the 
mind  is  emancipated  from  the  necessity  of  continuous  realization. 
Instead  of  this  intuitive  thinking,  or,  as  I  would  prefer  to  call  it,  this 
thinking  by  example,  we  may  think  by  signs,  either  perceived  or  im- 
aged, which  is  called  symbolic  thinking.8  As  Berkeley  remarks,9  "  It 
is  not  necessary,  even  in  the  strictest  reasonings,  that  significant 
names,  which  stand  for  notions,  should,  every  time  they  are  used, 
excite  in  the  understanding  the  ideas  they  are  made  to  stand  for. 
In  reading  and  discoursing,  names  are  used,  for  the  most  part,  as  sym- 
bolic letters  are  in  algebra,  in  which,  though  a  particular  quantity  be 
marked  by  each  letter,  yet,  to  proceed  right,  it  is  not  requisite  that 

T  See  Hamilton's  admirable  exposition  of  these  points,  Logic,  pp.  98,  99. 
8  Eori  fitv  ovv  TCI  iv  ry  (fiwpy  T&V  iv  ry  "fyv\y  TraQrjfJ-aTwv  ovf.ij3o\a. — Aristotle, 
De  Int.  ch.  i. 

'  See  Minute  Philosopher,  Dialogue  vii,  §  8. 


THE    TERM.  29 

in  every  step  each  letter  should  suggest  to  your  thoughts  that  par- 
ticular quantity  it  was  appointed  to  stand  for."  By  this  means  the 
facility  and  range  of  thought  are  vastly  increased. 

There  is  peculiar  danger,  however,  in  this  use  of  words  as  tempora- 
ry substitutes  for  thoughts.  Campbell  shows  that  by  it  many  judi- 
cious and  well-informed  persons  are  sometimes  led  to  talk  and  even  to 
write  nonsense  without  knowing  it.10  Thus,  one  might  trippingly,  or, 
as  we  say,  thoughtlessly,  speak  of  "a  bilinear  figure,"  or  "  an  involun- 
tary donation,"  or  say  "  the  weather  is  cold  as  blazes."  The  Psalm- 
ist corrected  himself :  "  I  said,  in  my  haste,  all  men  are  liars ;"  which 
was  well,  for  this  saying  included  him,  and  therefore,  if  true,  was  very 
likely  a  lie.  And  this  reminds  us  of  the  saying  of  Hobbes,  that 
"  words  are  the  counters  of  wise  men,  but  the  money  of  fools."  It 
is  consequently  needful,  says  Mansel,  at  the  end  of  a  process  of 
thought,  and  occasionally  at  intermediate  stages,  to  submit  the  result 
to  the  test  of  an  example,  and  ascertain  the  possible  coexistence  of 
the  attributes  in  a  corresponding  object  of  intuition.  The  existence 
of  a  class  is  possible  only  if  the  existence  of  the  individual  members 
is  possible;  hence  symbolical  cognition  supposes  intuitive  cognition 
actual  or  possible  as  its  condition,  and  derives  its  validity  from  it. 
The  test  of  thought,  then,  as  a  possibility,  is  an  image  of  an  example, 
which  is  possible  only  in  the  absence  of  self-contradiction.  We  must, 
then,  envisage  our  notions,  look  them  in  the  face,  and,  thus  realizing 
them,  insure  that  they  do  not  involve  contradictory  attributes.  This 
is  done  by  the  intuition  of  a  case,  or  an  example,  called,  by  the  Ger- 
mans, Anschauung,  which  may  well  be  translated  an  envisaging.11 

Symbolic  conception,  then,  is  that  in  which  an  arbitrary  sign  pres- 
ent to  sense  or  imaged  by  the  mind,  and  associated  with  the  attributes 
of  a  general  notion,  is  regarded  as  significant  of  all  the  members  of 
the  class. 

As  employed  in  symbolic  thinking,  the  concept  may  now  be  de- 
fined as  a  collection  of  attributes  united  under  a  sign,  and  represent- 
ing possible  objects  of  intuition. 


10  Philosophy  of  Rhetoric,  bk.  ii,  ch.  vii. 

11  Prolegomena  Logica,  p.  35  sq.  and  p.  106.     See  also  Hamilton's  Logic,  Lect- 
ure X. 


30  OF    CONCEPTS. 


II.  QUALITY. 

§  1.  Concepts  may  be  viewed  in  four  ways.  First,  with  reference 
to  the  things,  the  external  objects  which  they  represent,  and  in  which, 
directly  or  indirectly,  they  originate,  they  are  considered  as  arising 
from  them  as  their  source ;  as  constituted  of  the  marks  or  qualities  of 
the  things ;  as  applicable  to  one  thing,  or  common  to  many :  this  is 
their  Origin.  Secondly,  with  reference  to  the  mind,  or  thinking  sub- 
ject, they  are  considered  as  having  gradations  towards  perfection ;  as 
being  more  or  less  clear,  distinct,  etc. :  this  is  their  Quality.  Thirdly, 
with  reference  to  their  contents,  they  are  considered  as  comprehending 
marks,  or  as  extending  to  things :  this  is  their  Quantity.  Fourthly, 
with  reference  to  each  other,  they  are  considered  in  reciprocal  rela- 
tions as  the 'same  or  different,  as  containing  or  contained,  as  co-ordinate 
or  subordinate :  this  is  their  Relation.  Their  Origin  having  been 
considered  under  the  previous  topic,  we  come  now  to  examine,  sec- 
ondly, their  Quality. 

§  2.  Leibnitz  first  thoroughly  discussed  the  quality  of  concepts.  His 
views  were  expressed  in  a  famous  little  tract  "  On  Knowledge,  Truth, 
and  Ideas." *  In  it  he  pointed  out  the  distinction,  already  examined, 
between  intuitive  and  symbolic  thinking,  which,  according  to  Hamilton, 
superseded  in  Germany  the  whole  controversy  between  Nominalism  and 
Conceptualism  that  agitated  France  and  England  for  several  centuries. 

Concepts  have  quality  according  as  they  more  or  less  perfectly  rep- 
resent in  consciousness  their  objects.  The  following  scheme  marks 
the  degrees  by  which  knowledge  approaches  perfection : 

(  Obscure 

Knowledge  is....  •<  (  Confused2         (  Inadequate 

'(  Clear. . . .  4  (  "j  Adequate    ) 

(Distinct....-]  [-Perfect. 

(    (  Intuitive      ) 
{  Symbolic 

1  In  Ada  Eruditorum,  1684.      See  a  translation  of  the   tract  appended  to 
Baynes's  edition  of  the  Port-Royal  Logic. 

2  It  would  be  better,  perhaps,  if  this  were  named  Indistinct,  and  then  Confused 
might  be  taken  as  a  genus  to  include  Obscure  and  Indistinct. 


QUALITY.  31 

§  3.  Knowledge  is  first  obscure,  then  clear.  A  concept  is  obscure 
when  our  apprehension  of  it  is  so  faint  that  we  cannot  separate  it  from 
others.  E.  g.,  My  notion  of  tuberose  is  obscure,  even  if  not  mistaking 
it  for  a  kind  of  rose.  I  have  seen  it,  perhaps,  but  cannot  form  an 
image  of  it  sufficient  to  clear  it  from  my  notion  of  lily,  fuchsia,  and 
other  flowers  that  may  resemble  it.  My  notion  of  final  cause  is  ob- 
scure if  I  do  not  separate  it  from  material  cause,  formal  cause,  and 
efficient  cause.  So  the  vulgar  notions  of  value,  price,  utility,  capital, 
rent,  etc.,  are  each  obscure. 

We  think  a  concept  clearly  when  we  can  distinguish  it  as  a  unity, 
as  a  whole  in  complete  separation  from  other  wholes.  Clearness  is 
obtained  by  negative  judgments,  denying  or  setting  off  other  concepts 
apart  from  this  one,  or  by  remarking  the  specific  difference.  E.  g.,  We 
have  a  clear  knowledge  of  the  faces  of  our  friends,  since  we  readily 
know  one  from  another.  So  we  have  a  clear  notion  of  horse  when  we 
know  that  it  is  not  mule,  nor  ox,  nor  ass,  etc.  So  our  knowledge  of 
justice  is  clear  when  we  know  that  it  is  neither  truth,  nor  benevo- 
lence, nor  wisdom,  nor  power.  The  clearness  increases  according  as 
we  are  able  to  deny  of  a  notion  or  set  off  those  notions  which  lie 
nearest  to  it.  Again,  our  notion  of  perfume  is  cleared  by  remarking 
its  specific  difference ;  it  is  something  that  can  be  smelled. 

§  4.  Clear  knowledge  is  confused,  and  then  distinct.  I  have  a  clear 
knowledge  of  my  friend,  yet  that  knowledge  is  confused  or  indistinct, 
since  I  cannot  tell  how  or  by  means  of  what  I  know  him,  I  cannot 
describe  his  features.  The  artist,  however,  who  painted  his  portrait 
knows  distinctly  his  several  features.  Sometimes  an  artist  can  pro- 
nounce, clearly  that  a  work  of  art  is  badly  done  without  being  able  to 
give  a  reason  for  his  judgment.  His  notion  is  confused;  he  says 
there  is  something  in  it,  he  cannot  tell  what,  that  is  wrong.  My  no- 
tion of  gold  is  confused.  I  cannot  characterize  distinctly  either  its 
qualities  or  its  varieties. 

A  concept  is  distinct  when,  viewed  as  a  plurality,  we  can  discrimi- 
nate the  marks  that  constitute  it;  being  confused  so  long  as  these 
marks  are  indistinguishable.  Distinctness  is  obtained  by  affirmative 
judgments.  Analytic  abstraction  precedes,  and  is  followed  by,  a  syn- 
thesis,— the  mark  is  affirmed  of  the  thing.  Thus  the  marks  become 
severally  known,  and  we  can  thereafter  discriminate  them.  The 
knowledge  is  then  distinct.  It  is  natural  and  logical  when  one  un- 
dertakes to  explain  any  obscure  matter,  that  he  should  begin  by  clear- 


32  OF    CONCEPTS. 

ing  it,  especially  of  those  things  that  lie  nearest  to  it,  declaring  it  is 
not  these,  and  then  proceed  to  render  it  distinct  by  stating  -what  it  is. 
E.  g.,  Justification  is  not  pardon,  it  is  righteousness,  etc.3 

Distinctness  of  thought  has  two  modes.  We  think  a  concept  dis- 
tinctly when  we  distinguish  the  marks  which  it  connotes  from  each 
other, — this  is  its  distinctness  in  intension ;  and,  again,  when  we  can 
distinguish  the  things  which  it  denotes  from  each  other, — this  is  its 
distinctness  in  extension.  Intensive  distinctness  is  obtained  by  defi- 
nition, the  enumeration  of  the  marks.  Extensive  distinctness  is  ob- 
tained by  division,  which  discovers  the  things  contained  under  the 
concept.  Thus,  a  chemist's  notion  of  gold  is  distinct :  he  can  both 
name  its  marks,  i.  e.,  give  its  intension,  and  name  its  varieties  (if  va- 
rieties there  be),  i.  e.,  give  its  extension.  My  notion  of  thought  was 
obscure  until  I  separated  it  clearly  from  perception,  memory,  and  im- 
agination, and  it  is  now  becoming  distinct  by  studying  its  characters 
and  kinds.  Our  notion  of  red  is  very  clear,  but  intensively  indistinct ; 
we  cannot  name  the  particulars  by  which  we  distinguish  it  from  blue. 
It  is,  however,  extensively  somewhat  more  distinct,  as  we  can  name 
the  varieties  scarlet,  crimson,  pink,  etc.  A  primitive  notion,  such  as 
identity,  being  ultimate,  cannot  be  analyzed,  is  without  marks,  is  there- 
fore indefinable,  and  can  be  cognized  only  per  se.  Though  perfectly 
clear,  it  has  no  distinctness,  either  intensive  or  extensive. 

§  5.  Distinct  knowledge  is  inadequate,  then  adequate.  We  think  a 
distinct  concept  adequately  when  the  relative  number  and  importance 
of  the  marks  which  it  connotes  are  sufficient  to  correctly  represent  the 
things  which  it  denotes.  "  When  everything,"  says  Leibnitz,  "  that 
enters  into  a  distinct  notion  is  distinctly  known,  when  the  last  analysis 

3  If  we  would  understand  Leibnitz,  we  must  keep  in  mind  that  he  does  not  dis- 
tinguish kinds  of  knowledge,  but  degrees,  and  that  these  graduate  insensibly  into 
each  other.  When  I  discern  in  an  object  some  one  quality  which  another  has  not, 
this  may  be  sufficient  ground  for  me  to  declare  that  they  are  two,  the  one  is  not 
the  other,  and  so  far  my  knowledge  is  clear.  But  this  would  not,  perhaps,  be  suf- 
ficient ground  for  me  to  describe  the  object ;  I  cannot  yet  tell  what  it  is,  and  my 
knowledge  is,  therefore,  still  indistinct  or  confused.  But  as  I  discern  more  and 
more  marks,  my  knowledge  of  the  object  gradually  passes  from  what  we  call  mere- 
ly clear  but  indistinct,  into  distinct  knowledge,  and  I  can  then  describe  it.  When 
the  distinctness  becomes  more  complete,  I  can  define  it  inadequately,  but  not  until 
all  its  marks  are  discerned  can  I  define  it  adequately,  i.  e.,  enumerate  all  its  dis- 
tinctive marks.  The  whole  process  from  obscurity  to  perfection  consists  in  a  dis- 
cerning of  more  and  more  marks. 


QUALITY.  33 

is  reached,  then  the  knowledge  is  adequate,  of  which  I  scarcely  know 
whether  a  perfect  example  can  be  offered;  the  knowledge  of  numbers^ 
however,  approaches  near  to  it."  Perhaps  we  have  a  nearly  adequate 
knowledge  of  a  chess-board,  its  definition  consisting  of  so  few  marks, 
and  they  so  nearly  ultimate  and  simple :  a  square  composed  of  sixty- 
four  equal  squares  of  alternately  opposite  colors.  Dr.  Thomson  says, 
"  We  may  consider  any  knowledge  adequate  which  carries  the  analysis 
sufficiently  far  for  the  purpose  in  view."  E.  g.,  A  machinist  has  an  ad- 
equate knowledge  of  the  machines  he  has  invented,  constructed,  and 
used.  But  this  is  practical,  not  logical,  adequacy.  The  great  bulk  of 
our  knowledge  is  logically  inadequate. 

§  6.  Distinct  knowledge  is  also  either  intuitive  or  symbolic.  We 
think  a  distinct  concept  intuitively  when  we  image  an  example,  an  in- 
dividual, containing  in  it  all  the  marks  connoted  by  the  concept,  and 
itself  contained  under  the  class  of  things  denoted  by  the  concept.  No- 
tions not  very  complex,  and  especially  those  of  visual  objects,  arc 
readily  exemplified  in  an  image ;  but  when  one  is  very  complex,  we 
are  not  able  to  image  it  completely.  Thus  we  could  not  image  a 
chiliagon.  Even  were  some  such  figures  before  the  eye,  we  could  not 
perceive  the  difference  between  one  of  1000  sides  and  one  of  1001  sides. 
u  When,  however,"  says  Leibnitz,  "  we  are  able  wholly,  or  at  least  to 
a  great  extent,  to  form  this  image,  I  call  the  knowledge  intuitive." 

**  But,  for  the  most  part,"  he  continues,  "  especially  in  longer  analy- 
ses, we  do  not  behold  at  a  glance  the  whole  nature  of  a  thing,  which 
would  be  intuitive  knowledge,  but  we  employ  signs  instead  of  things. 
We  commonly  omit,  for  the  sake  of  expedition,  any  explication  of  these 
signs  in  present  thought,  knowing  or  believing  that  we  have  such  expli- 
cation in  our  power.  Thus,  when  I  think  of  chiliagon,  a  polygon  of  a 
thousand  equal  sides,  I  do  not  always  expressly  consider  the  nature  of 
'  side,'  of  '  equality,'  of  '  a  thousand,'  but  I  employ  these  words  in  the 
place  of  the  ideas  which  I  have  concerning  them."  This  is  symbolic 
thinking.  All  large  numbers,  such  as  those  which  state  the  velocity  of 
light  (186,000  miles  per  second),  the  distance  of  the  sun  (91  millions  of 
miles),  and  also  all  such  very  complex  notions  as  religion,  civilization, 
the  English  constitution,  war,  etc.,  are  known  to  us  only  symbolically. 
Our  knowledge  of  primitive  notions,  as  unit,  is  readily  intuitive,  while 
our  knowledge  of  composite  ones  is,  for  the  most  part,  symbolical.4 

4  Leibnitz  was  not  the  first,  as   Hamilton  and   Thomson  intimate,  who  re- 


34  OF  eoxc^rrs, 

§  V.  If  knowle'clg'e  be  at  the  same  time  both  adequate  and  intuitive, 
it  is  perfect.  We  think  a  concept  perfectly  when  it  is  clear,  distinct, 
adequate,  and  individualized  in  an  intuitive  example.  It  is  evident 
that  knowledge  logically  perfect  is  hardly,  or  only  in  rare  cases,  at- 
tainable by  the  human  mind.  But  we  are  too  easily  content  with  ob- 
scure or  indistinct  knowledge,  and  thus  our  thoughts  are  often  vague, 
or  even  self-contradictory  and  absurd,  without  our  becoming  aware  of 
it.  Then  we  believe  that  we  see,  when  really  we  are  blind. 

But  should  our  concepts  become  logically  perfect,  still  our  knowl- 
edge would  be  very  far  from  absolute  perfection.  "  Truth,"  savs  Cud- 
worth,  "is  bigger  than  our  minds,  and  we  are  not  the  s-ime  with  it, 
but  have  a  lower  participation  only  of  the  intellectual  nature,  and  arc 
rather  apprehendcrs  than  comprehenders  thereof.  This  is,  indeed,  one 
badge  of  our  creaturely  state,  that  we  have  not  a  perfectly  compre- 
hensive knowledge,  nor  even  such  as  is  adequate  and  commensurate  to 
the  essence  of  things."  Yet  it  is  the  ability  to  form  concepts  of  things, 
to  comprehend  and  understand  the  many  in  one,  to  classify  and  arrange 
in  order  of  relations  the  objects  of  knowledge,  that  is  above  all  other?, 
the  great  power  of  intellect,  the  glory  of  the  human  mind,  and  that 
which  constitutes  its  immeasurable  superiority  over  the  brute.  But, 
on  the  other  hand,  it  is  the  necessity  of  forming  concepts  at  all,  the 
necessity  of  resorting  to  a  fiction  of  unity  in  plurality,  the  necessity 
of  making  a  minute  part  stand  for  a  vast  whole,  that  marks  the  im- 
perfection and  finite  character  of  the  human  mind.  However  perfect- 
ly this  may  be  done,  it  is  merely  the  perfection  of  a  logical  device, 
not  the  perfection  of  knowledge.  To  know  things  in  any  measure, 
the  human  mind  must  think  them,  and  this  constitutes  its  immeasur- 
able inferiority  to  the  divine  mind,  which  does  not  think  at  all,  but 
knows,  by  the  immediate  intuition  of  the  things  themselves,  all  things, 
at  once  in  their  real  plurality  and  totality. 


marked  this  distinction  between  intuitive  and  symbolic  thinking,  though  certainly 
he  impressed  it  on  modern  philosophy.  I  find  the  same  distinction  clearly  implied 
by  Aristotle,  in  De  Soph.  Elencli.  ch.  i,  as  follows :  "  Not  being  able  to  point  out 
the  things  themselves  that  we  reason  about,  we  use  names  instead  of  the  realities 
as  their  symbols.  Then  the  consequences  in  the  names  appear  to  be  consequences 
in  the  realities,  just  as  the  consequences  in  the  counters  appear  to  the  calculator 
to  be  the  consequences  in  the  objects  represented  by  the  counters.  As,  in  calcula- 
tion, those  who  are  unskilled  in  manipulating  the  counters  are  deceived  by  those 
who  are  skilled,  so,  in  reasoning,  those  who  are  unacquainted  with  the  power  of 
names  are  deceived  by  paralogisms."  See  supra,  pp.  28,  29. 


QUANTITY.  35 


III.  QUANTITY. 

§  1.  We  are  next  to  consider  concepts  with  reference  to  their  con- 
tents, a  view  lying  more  strictly  within  the  province  of  Logic  than  the 
two  preceding,  which  belong  rather  to  Psychology.  That  a  concept 
may  be  viewed  as  a  quantity  is  manifest,  since  it  consists  of  a  variable 
plurality  of  marks,  and  is  applicable  to  a  variable  plurality  of  things. 
And  this  indicates  that  the  quantity  is  twofold.  It  is  either  an  in- 
tensive or  an  extensive  quantity.  A  concept  viewed  intensively  is  said 
to  connote  its  marks,  which  are  reduced  to  unity  in  thought  by  being 
conceived  as  inhering  in  one  substance ;  viewed  extensively,  the  con- 
cept is  said  to  denote  its  objects  or  things,  which  are  reducid  to  unity 
in  thought  by  being  conceived  as  constituting  one  class  or  group, 
each  member  of  the  class  possessing  all  the  marks.  Its  marks,  then, 
constitute  the  connotation  of  a  concept;  its  objects  constitute  the  de- 
notation of  a  concept.1 

The  intension  of  a  concept,  or  its  comprehension  or  depth,  is  de- 
termined by  the  greater  or  smaller  number  of  marks  contained  in  it, 
and  of  which  it  is  the  sum.  For  example,  the  concept  man  is  com- 
posed of  the  marks  existing,  living,  sentient,  rational,  all  thought  as 
inhering  in  one  substance.  This  explication  of  the  connotation  of  the 
concept  man  is  its  determination  or  definition ;  thus,  Man  is  a  being, 
living,  sentient,  and  rational. 

The  extension  of  a  concept,  or  its  sphere  or  breadth,  is  determined 
by  the  greater  or  smaller  number  of  specific  concepts,  or  of  objects 
contained  under  it.  For  example,  the  concept  man  contains  under  it 
the  specific  concepts  logician,  chemist,  artist,  mechanic,  etc.  Again,  the 

1  This  important  distinction,  though  taken  in  general  terms  by  Aristotle,  es- 
caped the  marvellous  acuteness  of  the  schoolmen,  and  remained  totally  overlooked 
until  the  publication  of  the  Port-Royal  Logic,  1662.  It  was  therein,  for  the  first 
time  in  modern  philosophy,  taken  and  applied  by  Arnauld,  with  whom  it.  was 
doubtless  again  original.  It  passed  thence  into  most  of  the  subsequent  works  on 
Logic.  In  Germany  the  doctrine  was  developed,  but  in  England  nothing  beyond 
Arnauld's  exposition  was  attempted  until  Hamilton  expounded  and  applied  it,  bor- 
rowing largely  from  Krug,Esser,  and  other  German  writers,  as  an  integral  part  of 
the  science.  That  he  overestimated  its  consequences  will  be  seen  in  the  sequel. 


36  OF    CONCEPTS. 

concept  logician  contains  under  it  the  objects  Aristotle,  Porphyry, 
Boethius,  Arnauld,  Hamilton,  and  the  rest.  This  explication  of  the  de- 
notation of  a  concept  is  its  specification  or  division. 

Observe  that  while  both  quantities  are  said  to  contain,  a  concept 
viewed  intensively  is  said  to  contain  in  it,  or  to  comprehend,  marks, 
but  viewed  extensively  it  is  said  to  contain  under  it  other  concepts,  or 
things. 

§  2.  It  is  evident  that  if  the  number  of  marks  constituting  the  con- 
tent of  a  concept  be  few,  it  may  extend  to  a  great  number  of  things ; 
and,  on  the  other  hand,  if  the  marks  are  many  and  distinctive,  the 
concept  can  include  and  be  predicated  of  only  a  small  number  of  things. 
Thus  the  concept  bird  has  only  a  few  marks,  such  as  existing,  living, 
sentient, feathered,  winged,  biped,  etc.;  but  it  is  applicable  to,  or  con- 
tains undcl'  it,  a  great  variety  or  number  of  things ;  whereas  the  con- 
cept dudf\i9&  more  marks,  such  as  ivcb-footcd,  etc.,  and  the  variety  or 
number  of  things  thereby  denoted  is  less.  Hence  we  have  the  gen- 
eral law  that  the  greater  the  intension,  the  smaller  the  extension  ;  and 
the  smaller  the  intension,  the  greater  the  extension ;  or,  in  other 
words,  the  two  quantities  arc  in  inverse  ratio. 

Concepts  are  modified  in  thought  by  changing  their  content.  Think- 
ing in  marks,  we  think  out  things,  and  vice  versa.  In  theoretical  strict- 
ness, the  thinking  in  one  mark  is  the  thinking  out  one  class  or  thing, 
and  vice  versa,  and  the  ratio  is  exact;  but  in  actual  thought,  owing  to 
the  incompleteness  of  our  concepts,  the  ratio  is  very  far  from  exact,  and 
the  law  applies  only  in  a  loose,  general  sense.  The  theoretical  state- 
ment, however,  should  be  limited  to  the  essential  and  original  marks, 
and  does  not  refer  to  the  accidental  and  the  derivative.  Original 
marks  carry  their  derivatives  along  with  them  by  necessary  implica- 
tion. The  latter,  therefore,  do  not  really  increase  the  intension,  but 
only  render  it  more  explicit. 

It  follows  from  the  above  that  the  minimum  of  intension  is  the 
maximum  of  extension.  A  concept  in  which  the  intension  or  depth 
is  a  minimum  is  one  in  which  a  plurality  of  marks  can  no  longer  be 
distinguished,  i.  e.,  it  has  but  one  mark.  Such  a  concept  is  being  or 
thing,  which  connotes  only  the  mark  existing.  It  is  called  a  simple 
concept  as  opposed  to  complex  or  compound.  Now  the  extension  or 
breadth  of  a  simple  concept  is  at  a  maximum.  Thus  the  concept 
being  or  thing  contains  under  it,  or  extends  to,  everything  that  exists, 
everything  in  the  universe. 


QUANTITY.  37 

On  the  other  hand,  the  minimum  of  extension  is  the  maximum  of 
intension.  A  concept  in  which  the  extension  or  sphere  is  at  a  mini- 
mum is  one  in  which  a  plurality  of  objects  can  no  longer  be  distin- 
guished, i.  e.  it  includes  in  its  sphere  or  applies  to  but  one  object.  Such 
a  concept  is  Aristotle,  or  Hadrian's  tomb,  or  Virginia,  or  the  sJcy^  or  to- 
day's lecture.  Each  of  these  denotes  only  one  object,  and  is  called  an 
individual,  because  it  cannot  be  logically  divided.  Now  the  intension 
or  comprehension  of  an  individual  is  at  a  maximum.  Thus  the  con- 
cept Aristotle  contains,  or  conceivably  contains,  in  it,  or  comprehends, 
an  indefinite  plurality  of  marks,  so  numerous  as  to  defy  all  computa- 
tion ;  a  number  which,  theoretically,  is  equal  to  the  number  of  the 
things  in  the  universe. 

§  3.  Under  a  previous  topic  it  was  said  that  an  abstract  term  is 
the  name  of  a  mark  thought  as  a  thing.  This  is  a  device  of  thought, 
bringing  mere  qualities  into  a  form  which  enables  us  to  make  them 
the  subjects  of  judgments.  A  quality,  being  thus  treated  as  a  concept, 
must  be  thought  as  itself  possessing  the  two  quantities  intension  and 
extension ;  that  is  to  say,  an  abstraction  is  both  connotative  and  de- 
notative. 

A  compound  quality  thought  as  an  abstraction  connotes  its  com- 
ponents. E.  g.,  "  The  wisdom  (abstract)  that  is  from  above  is  first  pure, 
then  peaceable,  gentle,  easy  to  be  entreated,  full  of  mercy  and  good 
fruits;  without  partiality,  and  without  hypocrisy."  Here  both  posi- 
tive and  negative  elements,  which,  taken  together,  compose  wise,  are  at- 
tributed to  wisdom  as  its  intension  or  connotation;  they  are  its  marks. 
Now  we  may  say,  Charity  is  wisdom  from  above,  and  thus  convey  into 
it  (connotare),  or  attribute  to  it,  all  these  marks.  Again,  an  abstrac- 
tion denotes  its  several  kinds.  The  wisdom  just  described  is  one 
kind.  But  we  arc  told  there  is  another,  and  that  "This  wisdom  de- 
scendeth  not  from  above,  but  is  earthly,  sensual,  devilish." a  There 
are,  then,  at  least  two  kinds  of  wisdom,  and  these  constitute  its  exten- 
sion or  denotation.  It  is  evident  that  the  kinds  denoted  by  an  ab- 
straction are  themselves  abstract  notions;  whence  it  follows  that  an 
abstraction  can  be  predicated  only  of  another,  as  Charity  is  wisdom. 

Evidently  these  marks  of  the  abstraction  may  be  attributed  to  the 
concrete  notion.  The  above  marks  may  be  affirmed  of  "  The  spirit- 

3  Epistle  of  Jamce,  iii,  15  and  17.  See  also  1  Cor.  from  i,  17  to  ii,  16,  where 
St.  Paul  discusses  several  kinds  of  wisdom. 


38  OF    CONCEPTS. 

ually  wise,  or  of  the  carnally  wise  man."  Bat  an  abstract  lias  quali- 
ties that  do  not  belong  also  to  the  concrete.  E.  g.,  "The  wisdom  that 
cometh  from  above  is  more  precious  than  rubies,  more  to  be  desired 
than  gold,  is  a  defence  better  than  strength,  better  than  weapons  of 
war."  This  cannot  be  said  of  "The  spiritually  wise  man."  The  ab- 
straction, then,  connotes  a  new  series  of  marks.  What  is  this  series? 
It  does  not  consist  of  the  component,  derivative  marks,  but  of  original 
marks,  attributable  to  the  quality  merely  as  a  quality :  e.  g.,  AVisdom 
is  desirable,  ennobling,  and  rare ;  that  is,  it  is  a  desirable,  ennobling, 
and  rare  quality.3  With  the  first  series  the  abstraction  is  not  so  com- 
plete, so  absolute,  as  with  the  second,  wherein  the  mark  is  viewed 
more  thoroughly  as  a  thing.  Many  more  things,  therefore,  can  be 
said  of  the  abstract  than  of  the  concrete  notion,  which,  perhaps,  is 
one  reason  of  the  favor  shown  it  by  thinkers.  A  primitive  notion, 
such  as  single,  having  no  components,  is,  when  taken  abstractly,  without 
the  first  series.  We  can  say  of  singleness  or  unity  only  those  things 
belonging  to  the  second  series. 

§  4.  It  has  been  already  stated  that  we  may  think  a  predicate  either 
as  a  mark  or  as  a  class ;  as,  Facts  are  stubborn,  or,  arc  stubborn  things. 
The  one  we  may  call  thinking  in  the  intensive  quantity ;  the  other, 
thinking  in  the  extensive  quantity.  It  is  true  that  one  quantity  im- 
plies the  other,  and  we  do  not  think  the  one  without  at  the  same  time 
thinking  the  other.  But  in  ordinary  thinking  one  of  two  is  in  vivid 
consciousness,  while  the  other,  though  within  consciousness,  is  com- 
paratively, and  it  may  be  very,  obscure.  Now  either  phase  of  think- 
ing may  become  habitual,  one  person  more  attentively  considering 
the  qualities  of  a  thing,  another  regarding  it  as  a  member  of  a  class. 
I  am  inclined  from  observation  to  believe  that  thinking  in  intension 

3  Mill,  in  his  Logic,  bk.  i,  ch.  ii,  §  5,  says  :  "  A  non-connotative  term  is  one  which 
signifies  a  subject  only  (e.  g.,  a  proper  name),  or  an  attribute  only.  Whiteness, 
length,  virtue,  signify  an  attribute  only.  None  of  these  names,  therefore,  are  con- 
nctative."  But  is  not  prudence  a  virtue  ?  He  afterwards  modifies  this  statement, 
saying :  "  Even  abstract  names,  though  the  names  only  of  attributes,  may  in  some 
instances  be  justly  considered  as  connotative ;  for  attributes  themselves  may  have 
attributes  ascribed  to  them  ;  and  a  word  which  denotes  attributes  may  connote  an 
attribute  of  those  attributes."  His  example  is  the  word  "  fault ;"  equivalent  to 
"  hurtful  quality."  "  This  word  is  a  name  common  to  many  attributes,  and  con- 
notes '  hurtfulness,'  an  attribute  of  those  various  attributes."  E.  g.,  Slowness,  in  a 
horse,  is  a  fault.  This  means  that  the  quality  in  a  horse  which  receives  this 
name  is  a  hurtful  or  undesirable  quality. 


QUANTITY.  39 

is  more  usual  with  cultivated,  and  in  extension  with  uncultivated,  per- 
sons. Compare  the  scholarly  synonyms  of  mark, — quality,  property, 
attribute,  characteristic,  etc.,  —  with  the  vulgar  synonyms  of  species^ 
— class,  sort,  kind  or  kin,  group,  variety,  set,  lot,  etc.  Children,  too, 
seem  to  prefer  extension ;  and  hence  pupils  in  Logic  usually  find  more 
difficulty  in  understanding  the  theory  relative  to  intension,  this  quan- 
tity being  less  familiar.  Also,  it  seems  that  the  literature  of  thought, 
from  the  early  days  of  Greek  philosophy  until  quite  modern  times, 
shows  a  strong  inclination  to  the  extensive  quantity,  describing  things 
by  classes ;  and  that  the  tendency  of  modern  thought  is  to  the  inten- 
sive quantity,  describing  things  by  attributes.  Certainly,  the  literature 
of  Logic,  from  Aristotle  to  Arnauld,  treats  exclusively  of  extension. 
Again,  this  appears  in  rude  languages  as  compared  with  the  refined, 
as  might  be  presumed ;  since  a  language,  in  its  early  stages,  gives 
common  names  to  things  in  groups,  as  sorts  or  kinds;  but  as  it 
progresses,  adjectives  multiply,  largely  derived  from  the  substantive 
nouns. 

If,  however,  these  are  facts,  they  would  seem  curiously  at  variance 
with  this  other  fact,  that  the  quantity  of  intension  is  given  at  once  in 
the  very  nature  of  things,  since  everything  has  qualities  which  can  be 
directly  apprehended;  whereas  the  quantity  of  extension,  the  distribu- 
tion of  things  into  genera  and  species,  does  not  exist  in  nature,  for 
nature  gives  only  individuals,  but  is  a  creation  of  mind  itself,  and  cre- 
ated only  through  the  quantity  of  intension.  The  intensive  quantity 
is  primary  and  natural ;  the  extensive,  secondary  and  factitious. 


40  OF    CONCEPTS. 


IV.  RELATION. 

§  1.  In  considering  the  reciprocal  relations  of  concepts,  we  will  view 
them  first  intensively.1  Notions  thus  viewed  are  identical  or  different. 
Of  notions  absolutely  identical  strictly  there  are  none;  for  unless 
there  be  some  difference,  they  cannot  be  distinguished,  and  are  there- 
fore one.  Indeed,  the  phrase  "  two  things  identical,"  taken  strictly, 
is  a  contradiction  in  terms.  Yet  in  Logic  we  speak  of  identical  no- 
tions, meaning  those  which,  having  reference  to  the  same  object,  differ 
only  in  being  conceived  by  different  minds,  or  by  the  same  mind 
at  different  times,  these  slight  differences  being  considered  as  not 
belonging  to  the  notion  itself.  Notions  whose  proper  differences 
arc  not  intrinsic  or  essential,  but  only  extrinsic  or  accidental,  are  rela- 
tively identical.  Such  notions  are  also  called  similar,  or  cognate;  and 
the  essential  attributes  being  all  common,  they  are  called  reciprocating 
or  convertible.  Thus  signs  taken  from  different  languages,  as  "  Com- 
passion and  sympathy,"  "Conspectus  and  synopsis,"  "Achromatic  and 
colorless,"  stand  often  for  similar  or  cognate  notions ;  and  the  terms 
of  a  definition,  as  "Grace  is  unmerited  favor,"  are  convertible  no- 
tions, for  each  comprises  the  same  essential  marks. 

Notions  are  absolutely  different  when  there  is  no  similarity.  Strict- 
ly there  are  none ;  but  the  term  is  loosely  applied  in  extreme  cases 
when  the  similarity  is  very  slight  and  unimportant,  as  in  "Blue  and 
heavy,"  or  "Money  and  memory."  Notions  are  relatively  different 
when  they  have  at  least  one  important  mark  common  and  one  di- 
verse; thus  "Saint"  differs  from  "Sinner,"  "Wise "from  "Unwise," 
"A  bright  day"  from  "A  dark  day." 

§  2.  Again,  notions  viewed  intensively  are  congruent,  incongruent, 
and  conflictive.  Congruent  notions  are  such  as  agree,  or  may  be  con- 
nected in  thought.  All  identical  notions  are  congruent;  also  many 
that  are  not  identical ;  as  "Learning  and  virtue,"  "Beauty  and  riches," 
"Magnanimity  and  stature;"  for  though  in  themselves  very  different, 

1  The  doctrine  is,  in  general,  Hamilton's,  drawn  mainly  from  Esser,  Krug,  and 
Drobisch.  Sec  Hamilton's  Logic,  pp.  150-158. 


RELATION. 


41 


they  can  easily  be  combined.  Incongruent  notions  are  such  as  can- 
not unite  in  the  same  object ;  as  "  A  loud  circle,"  "  A  bright  tooth- 
ache." Aristotle  puts  the  question  "Is  happiness  praiseworthy?"  To 
this  there  is  no  proper  answer,  for  it  has  no  proper  meaning.  It  is 
an  incongruous  jumble.  Notions  are  conflictive  when-  the  difference  is 
ciich  that  one  involves  a  negation  of  the  other ;  as  "  Virtue  arid  vice," 
"  Beauty  and  deformity,"  "  Wealth  and  poverty."  Such  notions  are 
said  to  be  in  opposition. 

Opposition  is  principally  of  two  kinds,  contradictory  and  contrary. 
Contradictories  are  only  two ;  and  to  affirm  or  deny  either,  denies  or 
affirms  the  other ;  both  cannot  be,  but  one  must  be ;  they  are  recipro- 
cal negatives;  as  "Bine  and  not-blue,"  "Walking  and  not-walking," 
"Jew  and  Gentile,"  "Simple  and  complex,"  "One  and  another,"  "A 
and  non-A,"  etc.  In  case  of  contradictory  opposition,  there  are,  by 
the  principle  of  Excluded  Middle,  only  two  conflictive  notions  con- 
ceivable. These  are  disjunct  notions.  Contraries  also  are  only  two; 
but  while  they  cannot  coexist,  it  may  be  that  neither  exists;  both 
may  be  denied  through  the  affirmation  of  something  else,  a  tertium 
quid.  Thus  "  White  and  black,"  "  Running  and  lying,"  etc.,  are  con- 
traries. A  color  may  be  neither  white  nor  black,  but  gray.  I  may 
be  neither  running  nor  lying,  but  sitting. 

In  order  to  define  contraries  more  exactly,  AVC  must  first  define  dis- 
parate notions.  These,  like  disjunct  notions  or  contradictories,  cannot 
be  associated  in  one  notion ;  they  exclude,  they  deny  each  other,  they 
are  conflictive.  They  differ  from  contradictories  as  contraries  were 
said  to  do ;  i.  e.,  it  may  be  that  neither  of  two  exists.  But  disparate 
notions  are  more  than  two.  They  constitute  a  series  of  co-ordinate 
notions  graduating  between  two  extremes ;  as  "  White,  graj,  black ;" 
"Running,  walking,  standing,  sitting,  lying;"  "Old,  middle-aged, 
young ;"  "  Day,  twilight,  night."  Now  the  two  extremes  of  a  dispa- 
rate scries  are  contrary  notions;  e.  g.,  "Day  and  night,"  "Wise  and 
foolish,"  "  Tall  and  short,"  "  Love  and  hate,"  "  Infinitely  great  and 
infinitely  small."  Aristotle,  in  the  Categories,  vi,  14,  says:  Contraries 
are  those  which  in  the  same  genus  are  most  distant  from  each  other. 

It  must  be  observed  that  pure  Logic  knows  nothing  of  disparates 
and  contraries,  as  they  necessarily  involve  matter.  When  we  abstract 
from  the  matter  of  a  notion,  and  consider  only  its  form,  it  is  impos- 
sible to  know  that  one  notion  opposes  another,  unless  one  is  the  mere 
negative  of  the  other,  as  A  and  non-A.  Therefore,  pure  Logic  knows 
no  opposition  between  notions  except  contradiction. 


42  OF    CONCEPTS. 

§  3.  We  note  one  other  distinction  between  concepts  viewed  in- 
tensively. As  comprehended,  they  are  either  involved  or  co-ordinate. 

One  concept  involves  another  when  the  latter  forms  a  part  of  the 
sum  of  the  marks  constituting  the  comprehension  of  the  former. 

Two  concepts  are  co-ordinate  when  they  are  coexclusive,  and  both 
immediately  comprehended  in  the  same  lower  concept. 

For  example :  Socrates  involves  both  famous  and  Athenian.  These 
arc  co-ordinate.  But  Athenian  further  involves  Greek;  and  Greek, 
European  ;  and  European,  human.  It  is  evident  that  these  latter  no- 
tions are  not  equally  proximate  and  immediate  in  "  Socrates,"  that 
some  are  given  only  through  others,  and  that  they  are  to  each  other 
in  the  relation  of  part  and  whole.  Thus  thought  evolves  the  simple 
out  of  the  complex ;  and  the  perfecting  of  knowledge  consists  in  this 
progressive  unfolding  into  clear  and  distinct  consciousness  the  inten- 
sion of  notions  originally  obscure  and  confused. 

In  speaking  of  concepts  as  involving,  and  of  marks  as  parts  of  a 
whole,  these  words  are  used  in  a  peculiar  sense.  The  parts  are  not 
partes  extra  partes,  for  each  mark  permeates  and  informs  the  whole 
concept.  Thus  when  I  think  of  chalk  as  both  white  and  brittle,  the 
whiteness  and  the  brittleness  arc  thought  to  coexist  throughout. 

§  4.  We  now  pass  to  a  consideration  of  the  relations  of  concepts  in 
the  quantity  of  extension,  which,  however,  be  it  constantly  kept  in 
mind,  is  but  a  different  aspect  of  the  same  thing.  These  relations  are 
of  three  sorts,  inclusion,  intersection,  and  exclusion. 

1st.  Of  Inclusion.  One  concept  is  included  in  another  when  the 
sphere  or  extent  of  the  one  coincides  with,  or  is  contained  under,  that 
of  the  other.  There  are  two  cases  of  inclusion : 

(a.)  Coextension ;  as  when  the  spheres  coincide  or  are  common. 
(b.)  Subordination ;  as  when  one  is  contained  under  the  other,  as 
a  species  under  a  genus,  or  as  an  individual  under  a  species. 

2d.  Of  Intersection.  Two  concepts  intersect  when  their  spheres 
have  a  common  part,  and  each  a  part  not  common. 

3d.  Of  Exclusion.     One  concept  is  excluded  from  another  when 

their  spheres  have  no  part  common.    There  arc  two  cases  of  exclusion : 

(a.)  Co-ordination  ;  as  when,  though  mutually  exclusive,  both  arc 

immediately  contained  under  the  same  concept. 
(6.)  Non-co-ordination :  as  when,  while  mutually  exclusive,  they 
are  not  both  immediately  contained  under  the  same  concept. 


RELATION. 

Let  us  now  restate  the  above,  and  symbolize  by  Euler's  circular 
notation,2  in  which  the  sphere  of  a  concept  is  represented  by  a  circle ; 
and  also  by  Hamilton's  linear  notation,3  in  which  the  extent  of  a  con-" 
cept  is  represented  by  a  horizontal  line ;  the  relation  of  two  or  more, 
by  such  lines  standing  one  under  the  other,  and  by  their  comparative- 
ly greater  or  less  extent ;  affirmation  being  expressed  by  a  vertical  line 
joining  two  horizontal  ones ;  negation,  by  the  absence  of  such  con- 
nection. 


Inclusion. 


Intersection, 


(  Coextension 


Subordination 


Exclusion . . 


Co-ordination 


Non-co-ordination         [  E  }  (  0 


Globe 


Sphere 


Animal 


Protestants 
Irish 


Wonpon 


Swortl       Spear 


Evolution 


Chance 


Of  these  relations  there  are  only  three  that  call  for  special  remark, 
— subordination,  intersection,  and  co-ordination.  Subordination  will 
be  treated  at  once ;  intersection  under  the  topic  Definition ;  and  co- 
ordination under  Division. 


§  5.  When  one  concept  is  subordinate  to  or  contained  under  an- 
other, it  differs  from  the  higher   concept  by  comprehending  more 

2  The  invention  of  this  method  of  sensualizing  the  logical  relations  of  concepts 
by  circles  is  usually  attributed  to  Euler,  who  made  use  of  it  in  his  Lettrcs  d  une 
PrinccKse  d'Allemagne,  1768.     It  is  found,  however,  in  a  posthumous  work  of 
Christian  Weise,  Rector  of  Zittau,  who  died  in  1708.     Ploucquet  employed  the 
square,  and  Haass  the  triangle,  instead  of  the  circle. — Drobisch's  Logic,  §  84 ;  see 
also  Thomson's  Outline,  §  104;  and  Hamilton's  Logic,  pp.  133  and  180. 

3  This  is  a  modification  and  an  improvement  of  Lambert's  linear  notation  as 
found  in  his  Neucs  Organon,  1764.     It  is  to  be  preferred  to  the  circular  notation. 
Both  represent  only  relations  in  extension,  not  those  in  intension,  and  therefore, 
though  convenient  and  helpful,  are  inadequate.     See  Hamilton's  Logic,  p.  670  sq. 


44  OF    CONCEPTS. 

marks  and  by  extending  to  fewer  individuals.  It  is  called  a  species. 
Thus  sword  is  a  species  of  weapon ;  man  is  a  species  of  animal. 
Sword  is  contained  under  iveapon  ;  it  comprehends  more  marks,  but 
it  extends  to  fewer  things ;  it  is  the  narrower  notion.  The  superior 
concept,  sinc3  it  contains  under  it  more  things,  is  the  more  general 
notion,  and  hence  is  called  the  genus.  Thus  weapon  is  the  genus  of 
sword ;  animal  is  the  genus  of  man.  The  notion  animal  extends  to 
many  things  besides  men  ;  it  is  the  broader  notion. 

It  is  manifest  that  genus  and  species  are  merely  relative  terms ;  for 
the  genus  may  be  contained  under  some  higher  concept,  and  then  rel- 
ative to  this  higher  genus  it  is  a  species.  Thus  weapon  is  a  species  of 
the  genus  instrument.  Of  course  the  species  may  contain  under  it 
some  lower  concept,  and  then  become  the  genus  of  that  lower  species. 
Thus  sword  is  a  genus  containing  under  it  the  lower  species  sabre, 
rapier,  etc.  A  concept  that  is  alternately  a  genus  relative  to  lower 
concepts,  and  a  species  relative  to  some  higher  concept,  is  called  a 
subaltern  genus. 

A  genus  is  a  universal  notion,  or  a  universe,  because  it  binds  a  plu- 
rality of  parts  into  the  unity  of  a  whole.  This  is  the  logical,  direct 
from  the  etymological,  meaning  of  universe,  ad  unum  versus.  A 
universe,  then,  means,  strictly,  E pluribus  unum.  It  is  called,  by  way 
of  eminence,  the  Logical  Whole.3  A  species,  since  it  is  but  a  part  of 
this  whole,  is  a  particular  notion.  We  should  distinguish  between  the 
usual  meaning  of  universe,  as  that  unlimited  highest  genus  which  com- 
prises all  things  in  one,  and  universe  considered  as  a  limited  genus 
which  unites  only  some  things. 

A  universe  or  genus  is  usually  present  to  the  mind  of  a  speaker, 
within  which  his  thoughts  revolve,  and  under  which,  often  without 
naming  it,  he  is  bringing  in  his  statements.  If  we  apprehend  his  as- 
sumed universe,  we  may  follow  and  understand  his  thoughts ;  if  not, 
confusion  is  inevitable  from  the  ambiguities  of  language.  Thus  the 
word  "  civil "  has  many  meanings ;  it  is  opposed  to  "  natural,"  to 
"  military,"  to  "  ecclesiastical,"  to  "  discourteous,"  and  so  on.  Now  if 
"  civil  service "  be  spoken  of,  and  it  is  apprehended  that  the  talk  is 
under  the  tacitly  implied  universe  of  "the  departments  of  govern- 
ment," then  we  understand  that  it  is  intended  to  exclude  "  military  " 
and  "  ecclesiastical,"  and  confusion  is  avoided.  In  rude  parlance  we 

3  "  Universale  totum  quoddam  est ;  quippe  multa  complectitur  ut  partcs.  Dici- 
tur  totum  logicum,  quia  logicce  munus  est  de  universis  disputare." — Burgersdjck. 


RELATION.  45 

say,  we  must  know  what,  in  general,  one  is  talking  about,  in  order  to 
understand  his  particular  statements. 

Both  genera  and  species  are  called  classes,  and  the  arrangement  of 
things  according  to  genera  and  species  is  called  classification.  The 
psychological  process  by  which  we  classify  has  been  somewhat  antici- 
pated in  the  account  given  of  generalization  and  specialization,  which 
terms  are  synonymous  with  generification  and  specification.  AVhen  we 
think  the  similar  to  be  the  same,  we  form  a  genus  including  all  the 
similar  things.  Thus  in  contemplating  man  and  brute  we  experience 
the  shock  of  similarity ;  we  abstract  from  each  what  is  similar ;  we 
think  it  the  same,  or  common  to  both ;  we  give  it  a  name,  and  thus 
establish  the  class,  the  genus,  animal,  containing  under  it  man  and 
brute  as  species.  On  the  other  hand,  when  we  think  the  dissimilar  to 
be  diverse,  we  form  a  species,  excluding  a  portion  of  the  things  con- 
sidered. Thus  in  contemplating  animals  we  experience  the  shock  of 
dissimilarity ;  we  abstract  from  man  the  quality  rational,  which  marks 
the  diversity ;  we  affirm  it  of  man  and  deny  it  of  the  rest.  Thus  we 
establish  two  species  of  animals,  the  rational  and  the  irrational,  or 
men  and  brutes. 

Finally,  the  species  as  parts  make  up  the  genus  as  a  whole.  These 
are  paries  extra  partes,  for  they  do  not  coexist,  as  do  marks,  but  are 
actually  separable  groups  of  things;  c.  g.,  diamonds  and  rubies  are 
species  of  jewels.  Consequently,  it  is  possible  to  symbolize  geomet- 
rically, by  circles  or  lines,  the  relations  of  concepts  viewed  in  exten- 
sion, which  is  not  practicable  when  they  are  viewed  in  intension. 

§  6.  It  should  be  observed  that  subordination  in  the  quantity  of 
extension  corresponds  to  involution  in  the  quantity  of  intension.  Also 
while  the  term  generalization  is  applicable  to  either  quantity,  the  term 
specification  relates  to  extension,  and  corresponds  to  the  intensive 
term  determination.  For  determination  is  a  thinking  in,  a  synthesis, 
a  concretion  of  marks,  and  this,  since  it  throws  out  things,  specifies 
a  concept.  Determination,  then,  restricts  the  denotation  by  ampli- 
fying the  connotation,  and  terminates  only  in  individualization. 

§  7.  Many  concepts  are  related  to  each  other  as  correlatives.  Ac- 
cording to  the  Law  of  Relativity,  knowledge  always  includes  two 
things.  We  know  heat  by  transition  from  cold;  light  by  passing 
out  of  the  dark  ;  up  by  contrast  to  down.  There  is  no  such  thing  as 
an  absolute  knowledge  of  any  one  property ;  we  could  not  know  mo- 


46  OF    CONCEPTS. 

tion  if  we  were  debarred  from  knowing  rest ;  our  first  parents  had  no 
knowledge  of  good  until  it  was  "  bought  dear  by  knowing  ill."  We 
may  be  thinking  more  of  one  member  of  the  couple  than  of  the  other, 
of  the  heat  rather  than  of  the  cold,  of  the  straight  line  rather  than  of 
the  crooked ;  but  if  either  exists,  the  other  always  coexists  with  it  in 
consciousness.  The  one  is  the  explicit,  the  other  the  implicit,  subject 
of  the  thought. 

This  would  seem  to  occasion  double  names  throughout  all  the  uni- 
verse of  things,  and  language,  if  complete,  would  contain  no  single 
.names,  but  consist  of  couples.  Accordingly  we  find  a  great  many 
couples,  specifically  called  "  Correlative  Terms,"  in  each  of  which,  if 
either  member  be  expressed,  the  other  is  implied;  as  "Parent  and 
child,"  "Ruler  and  subject,"  "Cause  and  effect,"  "Heavy  and  light," 
"Rich  and  poor,"  "Genus  and  species,"  "Positive  and  negative." 

The  last  example,  "  Positive  and  negative,"  "  To  affirm  and  to 
deny,"  is  probably  the  basis,  or  origin,  and  the  generalization  of  all 
the  rest.  One  of  the  two  has  usually  more  or  less  of  a  negative 
character ;  and  in  cases  where  names  have  not  been  adopted  for  both 
correlatives,  one  exists  in  thought  as  a  negative.  Hence  for  every  pos- 
itive'concrete  name  a  corresponding  negative  may  be  framed  as  cor- 
relative to  it  by  attaching  a  negative  particle,  such  as  the  prefixes 
un-,  in-,  and  the  suffix  -less  ;  as  "  Conscious  and  unconscious,"  "  Temper- 
ate and  intemperate,"  "  Godly  and  godless,"  "  A  and  non-A." 4 

§  8.  Another  mode  in  which  concepts  are  related  is  expressed  by 
the  old  and  almost  disused  logical  terms  First  Intention  and  Second 
Intention.6  A  first  notion  or  intention  is  a  concept  of  things  formed 
by  the  first  or  direct  application  of  the  mind  to  the  object.  It  de- 
notes things.  The  concepts  which  we  have  been  using  as  illustrations 
are  all  first  intentions.  The  object  Socrates  is  regarded  by  the  mind 
as  Greek,  man,  animal,  body,  etc.  A  mental  state  may  be  thought  as 
a  smell,  a  sensation,  a  feeling,  a  consciousness.  All  these  are  first  in- 
tentions. A  second  notion  or  intention  is  a  concept  generalized  from 
first  intentions.  It  denotes  first  intentions  or  concepts  of  tilings.  It 
is  the  conception  under  which  the  mind  regards  its  first  intentions 
as  related  to  each  other.  Thus  the  relation  of  animal  to  man,  and  of 


4  See  Bain's  Logic,  p.  2  and  p.  55. 

6 In-tendere.     "Ego  dico  intentionem  nil  aliud  esse  quam  attentionem  ac  dili- 
gentiam  animae  in  alicujus  rei  consideratione." — Zabarella,  De  Rcb.  Nat.  p.  871. 


RELATION.  47 

man  to  animal,  is  expressed  in  the  second  intentions  genus  and  species. 
These  are  concepts  of  concepts.  Adopting,  then,  the  definitions  of 
Mansel,  we  have  the  following : 

A  First  Intention  is  a  concept  of  a  thing  or  things,  formed  by  the 
mind  from  materials  existing  without  itself. 

A  Second  Intention  is  a  concept  of  other  concepts,  formed  by  the 
mind  from  materials  existing  within  itself. 

First  intentions  precede  in  order  of  time,  for,  as  Boethius  explains, 
men  first  intended  to  give  names  to  things  before  they  intended  to 
iind  names  for  their  mode  of  viewing  them.  The  first  is  the  real 
meaning  of  a  word,  the  second  is  its  logical  value.  "Of  the  first 
intention,"  says  Ilobbes,  "are  the  names  of  things;  of  the  second  are 
the  names  of  names  and  speeches."  This  is  the  true  distinction,  but 
marred  in  expression  by  the  ultranominalism  of  the  writer.6 

The  distinction  between  first  and  second  intentions  is  nearly  iden- 
tical with  that  between  matter  and  form.  Logic  is  not  occupied  with 
things  as  they  exist  in  nature,  but  with  the  way  the  mind  conceives 
them ;  not  with  matter,  but  with  form ;  not  with  first  notions,  but 
with  second.  Nearly  all  logical  terms  are  names  of  forms,  or  second 
intentions;  as  Universe,  Concept,  Mark,  Property,  Accident,  Defini- 
tion, Judgment,  Syllogism,  Subject,  Predicate,  etc.  Hence  Logic  is 
said  to  treat  of  second  intentions  applied  to  first ;  and  may  be  well 
defined  as  the  Science  of  Second  Intentions.  Avicenna,  the  Arabian 
philosopher,  in  Meta.  ch.  ii,  says,  "  Subjectum  Logicas  sunt  intentiones 
intellects  secundo,  qua3  apponuntur  intentionibus  primo  intellects, 
secundum  hoc  quod  per  eas  pervenitur  de  cognito  ad  incognitum." ' 

6  "  Prima  notio  est  conceptus  rei  quatcnus  est,  ut  animalis,  hominis ;   secunda 
notio  est  conceptus  rei  quatenus  intelligitur,  ut  subjectum  et  attributum." — Pacius. 

7  The  distinction  is  very  important,  and  seems  clear  enough,  but  has  been  re- 
markably mistaken.     Aldrich  misstates  it;  Whately  blunders  sadly  in  a  guess  at 
it,  but  with  admirable  candor  adds  in  a  note  (Logic,  p.  202),  "  I  must  confess  that, 
after  the  most  patient  attention  to  the  explanations  given  of  it,  I  have  never  been 
able  to  comprehend  what  is  meant  by  it."    We  are  indebted  chiefly  to  Mansel  (see 
notes  m  Aldrich,  pp.  20,  21)  for  clearing  away  the  mist.     See  also  Thomson's  Out- 
line, §  16.    It  seems  that  of  old  the  same  trouble  existed,  and  the  profane  used  to 
make  fun  of  the  venerable  scholastics  and  defame  their  darling  Second  Intentions 
with  such  burlesque  questions  as  this :  "  Utrum  chimaera  bombinaus  in  vacuo  posset 
comedere  secundas  intentiones  ?" 


48  OF    CONCEPTS. 


V.  DEFINITION. 

§  1.  In  order  to  give  to  our  thoughts  scientific  precision,  and  to 
systematize  them  into  a  scientific  whole,  we  must  perform  a  double 
operation.  First,  we  must  consider  what  we  think,  i.  e.,  what  is  com- 
prehended in  thought.  Secondly,  we  must  consider  of  what  and 
how  many  things  we  think,  i.  e.,  to  what  and  how  many  objects  the 
thought  extends.  The  comprehension  of  thought  is  developed  by 
Definition;  its  extension,  by  Division.  Our  thoughts  by  this  means 
are  rendered  distinct,  the  internal  or  intensive  distinctness  being  se- 
cured by  definition  ;  the  external  or  extensive  distinctness,  by  division. 
Thus  we  approximate  perfection  of  thought  (ii,  §  4). 

It  has  already  been  stated  that  definition  is  the  explication  of  the 
essential  and  original  marks  of  a  thought  or  concept  (iii,  §  1).  Thus, 
to  repeat  the  example,  Man  is  defined  as  rational,  sentient,  living,  ex- 
isting. It  is  manifest,  however,  that  this  mode  of  statement  is  aAvk- 
ward,  and  in  most  cases  impracticable.  Observing,  then,  that  the  no- 
tion animal  involves  sentient,  organized,  existing,  all  the  marks  that  arc 
common  to  man  with  other  concepts,  we  substitute  for  them  this  no- 
tion, and  define  summarily,  "  Man  is  rational  and  animal."  The  mark 
rational,  not  included  in  this  summation,  is  distinctive,  as  belonging 
to  man  alone  of  all  the  notions  that  connote  animal.  A  logical  defini- 
tion, then,  consists  of  two,  and  only  two,  essential  and  original  marks, 
one  of  which  is  common  and  the  other  distinctive. 

Since  the  notion  defined  contains  implicitly  the  marks  which  the 
definition  contains  explicitly,  it  follows  that  they  are  reciprocating  or 
convertible  concepts  (iv,  §  1),  Either  may  be  substituted  for  the 
other.  Thus,  "  A  triangle  is  a  polygon  of  three  sides,"  and  "  A  poly- 
gon of  three  sides  is  a  triangle."  Or,  as  "Every  rectilineal  figure 
may  be  divided  into  triangles  having  a  common  point,"  so  "  Every 
rectilineal  figure  may  be  divided  into  polygons  of  three  sides  having  a 
common  point." 

Simple  notions,  as  containing  no  plurality  of  marks,  are  incapable 
of  definition.  The  notion  being,  for  example,  having  only  one  mark, 
existing,  and  no  differential  or  distinctive  element,  is  an  indefinable,  an 
indefinite  notion.  It  is  distinguishable  only  from  nothing,  a  mere 


DEFINITION.  49 

empty  negation  having  no  content.  Indeed,  a  simple  notion,  having 
but  one  mark,  cannot  in  strictness  be  called  a  concept.  On  the  other 
hand,  an  individual  cannot  be  logically  defined,  since  practically  \ve 
cannot  form  a  notion  comprising  all  the  essential  and  original  marks 
which  it  has  in  common  with  any  other  notion  or  thing.  An  indi- 
vidual can  only  be  described. 

§  2.  It  is  obvious  that  definition,  according  to  the  above  account, 
relates  primarily  to  the  intension  of  a  concept.  The  scholastic  lo- 
gicians, however,  viewed  it  in  the  extensive  quantity,  and  their  view 
and  nomenclature  are  most  usual  with  us.  According  to  them,  a  defi- 
nition consists  of  the  proximate  genus  and  the  specific  difference. 
The  proximate  genus  is  that  class  under  which  the  notion  defined  is 
immediately  contained.  Thus  animal  is  the  proximate  genus  to  the 
concept  man.  The  specific  difference  is  that  which  distinguishes  the 
notion  defined  from  all  other  species  of  that  genus.  Thus  rational  is 
the  specific  difference  that  distinguishes  man  from  all  other  species 
contained  under  animal,  as  beasts,  birds,  fishes,  etc.  Let  it  be  re- 
marked that  rational  is  also  the  generic  difference,  since  it  distin- 
guishes the  notion  man  from  the  genus  animal.  Such  is  the  scho- 
lastic definition  per  genus  et  differentiam.  Other  examples  are:  "Snow 
is  frozen  (^specific  difference)  mist"  (  ==  proximate  genus);  "Logic 
is  the  science  (=p.  g.)  of  the  necessary  forms  of  thought"  (rrs.  d.) ; 
"Eloquence  is  the  power  of  influencing  men's  conduct  (=p.  g.)  by 
means  of  speech"  (  =  s.  d.). 

These  two  elements,  the  proximate  genus  and  the  specific  difference, 
make  up  the  whole  intension  of  every  notion,  for  the  proximate  genus 
connotes  all  the  marks  common  to  the  several  species.  But  to  make 
the  explication  complete,  it  is  further  necessary  to  define  the  genus. 
This  done,  the  same  necessity  again  appears,  and  is  met.  We  pro- 
ceed in  this  manner  until  we  reach  a  simple  notion  as  the  highest  and 
final  genus,  which  cannot  be  defined.  For  example : 

A  carnivore  is  a  flesh-eating  (  — d.)  mammal  (=g.). 

A  mammal  is  a  vertebrate  (=g.)  suckling  its  young  (  =  d.). 

A  vertebrate  is  an  animal  (=g.)  having  an  internal  skeleton  (=d.). 

An  animal  is  a  sentient  (  —  d.)  organism  (  =  £.)• 

An  organism  is  a  living  (=d.)  being  (  — g.)- 

Here  we  have  the  whole  connotation,  "  A  carnivore  is  flesh-eating, 
suck-giving,  internal-skeletoned,  sentient,  living,  existing." 

4 


50  0?    CONCEPTS. 

§  3.  Concepts  often  intersect  ;  that  is,  two  concepts  often  have  a 
common  part,  and  each  a  part  not  common.  There  are  Irish  Protes- 
tants ;  also  there  are  Irish  not  Protestants,  and  there  are  Protestants 
not  Irish.  Some  blacls.  things  are  heavy,  some  not;  some  heavy  things 
are  black,  some  not.  The  common  part  is  a  species  which  is  con- 
tained under  each  or  either  of  the  total  concepts  as  a  genus.  In  other 
words,  whenever  a  certain  group  of  things  may  be  referred  to  either 
of  two  genera,  these  genera  intersect,  the  group  being  a  common  part. 

Now  the  two  portions  of  a  definition,  the  genus  and  the  difference, 
may  be  each  viewed  as  a  concept  in  extension.  If  so,  they  will  be  seen 
to  intersect,  and  the  notion  defined  to  be  the  common  part.  Thus  the 
notion  rational  intersects  the  notion  animal  ;  man,  being  both,  is  the 
^_^^_^^  common  part  ;  while  there  are  animals  that  are  not  ra- 
/  A  \  tional,  as  the  beasts  of  the  field  ;  and  there  are  rational 

7?  I  Aft  A 

\  \)  j  beings  that  are  not  animals,  as  angels.  Ordinarily,  we 
think  of  man  as  an  animal,  bringing  him  under  this  no- 
tion as  a  proximate  genus  ;  and  we  use  the  mark  rational  as  a  specific 
difference  to  characterize  him,  to  mark  him  off  from  other  animals. 
But  it  is  perfectly  competent  to  refer  him  to  rational  being  as  the 
genus,  and  to  use  animal  as  the  differential  mark  ;  thus,  "  Man  is  a 
rational  being  (—p.  g.)  having  animal  nature"  (—  s.  d.).  Therefore 
the  two  portions  of  a  definition  are  convertible  in  thought,  and  it  de- 
pends wholly  upon  the  use  made  of  them  in  thought  as  to  which 
should  be  called  the  genus,  and  which  the  difference.  So,  if  a  watch 
is  a  portable  timepiece,  it  may  be  thought  either  as  a  sort  of  port- 
able thing  or  as  a  kind  of  timepiece  ;  if  a  concept  is  a  bundle  of 
marks,  it  may  be  thought  either  as  a  kind  of  bundle  or  as  meaning 
that  kind  of  marks  which  are  bundled  together.  Aristotle  observes 
that  specific  difference  is  of  the  nature  of  genus. 

§  4.  Since  a  definition  is  the  explication  of  all  the  connotation  of  a 
thought,  the  perfection  of  its  definitions  is  the  perfection  of  a  science. 
In  studying  a  prepared  science,  we  begin  with  the  definitions  ;  but 
in  constructing  a  science,  we  end  with  the  definitions.  True,  in  its 
early  stages,  we  necessarily  make  constant  use  of  provisional,  imperfect 
substitutes  ;  and  so  it  was  that  Socrates,  presiding  at  the  birth  of  sci- 
ence,1 spent  his  whole  life  in  searching  for  and  analyzing  definitions. 


1  The  mother  of  Socrates,  Phaenarete,  was  /mta,  a  midwife  ;  and,  in  allusion  to 
this,  his  method  of  eliciting  truth  by  questioning  was  called  the  maieutic  method. 


DEFINITION.  51 

But  as  a  science  progresses,  its  definitions  are  modified,  gradually  im- 
proved, and  made  real ;  and  when  they  are  finally  perfected,  the  sci- 
ence is  perfected. 

This  gives  occasion  to  distinguish  three  kinds  of  logical  definition 
per  genus  et  differentiam,  the  nominal,  the  real,  and  the  genetic.  This 
distinction  is  grounded  on  the  matter ;  pure  Logic,  as  it  treats  of  the 
form,  only,  does  not  know  kinds  of  definition.  Consequently,  if  we 
consider  the  form  only,  each  of  these  three  kinds  of  definition  exhibits 
the  proximate  genus  and  specific  difference.  When  we  look  into  the 
matter,  we  discover  such  variations  and  imperfections  as  justify  the 
above  distribution. 

Nominal  definitions  express  the  meaning  of  a  word  as  it  is  popu- 
larly understood  and  used,  not  explicating  all  the  marks  (since  com- 
mon usage  requires  much  less  than  exact  science),  and  freely  employ- 
ing those  that  are  accidental,  derivative,  or  peculiar.  Thus,  "A  pension 
is  an  allowance  for  past  services;"  "A  violin  is  a  musical  instrument 
having  four  strings  and  played  with  a  bow ;"  "  The  east  is  where  the 
sun  rises."  The  definitions  given  by  the  dictionaries  are  mostly  nominal. 
A  mere  heaping-together  of  synonyms,  as  "  Law  is  a  rule,  decree,  or 
statute,"  or  merely  giving  the  etymology,' as  "  Centaur"  means  "bull- 
goader,"  though  often  called  nominal  definitions,  are  obviously  no  defi- 
nitions at  all.  The  imperfect,  provisional  definitions,  spoken  of  above 
as  preliminary,  in  order  to  prepare  the  way  for  real  ones,  are  nominal 
definitions.8 

Real  definition  is  concerned  with  the  real  nature  of  things ;  it  un- 
folds all  the  essential  marks  in  their  original  form,  and  these  only, 
and  adds  none  that  are  not  implied  in  the  subject  defined.  It  is 
therefore  strictly  analytic.  Such  are  the  perfected  definitions  of  a  sci- 
ence. An  unexceptionable  example  can  hardly  be  found.  The  ex- 
actness of  mathematical  thought  gives  approximations.  Thus,  "  A 
circle  is  a  plane  figure  whose  periphery  is  everywhere  equidistant  from 
the  centre."  In  practice  the  distinction  between  the  nominal  and  the 
real  definition  cannot  always  be  clearly  descried.  They  graduate  into 

2  The  nominal  definition,  according  to  Aristotle,  is  one  in  which  there  is  no  evi- 
dence of  the  existence  of  the  object  to  which  the  definition  is  applicable ;  as  a  cen- 
taur. Subsequent  logicians,  especially  the  recent  ones,  differ  widely  from  Aris- 
totle and  from  each  other  in  stating  its  meaning  and  distinguishing  it  from  the 
real.  The  statement  in  the  text  agrees  with  some  of  the  best  authorities,  and 
seems  to  accord  best  with  popular  usage.  It  is  a  point  of  little  importance.  On 
the  whole  subject,  see  Hansel's  Appendix  to  Aldrich,  note  C. 


52  OF    CONCEPTS. 

each  other.  The  requisite  that  the  latter  shall  consist  of  the  essential 
and  original  marks,  which  constitutes  the  distinction,  evidently  relates 
exclusively  to  matter,  not  at  all  to  form.  Hence,  as  said,  pure  Logic 
knows  nothing  of  this  distinction. 

A  genetic  or  causal  definition  concerns  itself  with  the  rise  or  pro- 
duction of  a  thing;  considers  it,  not  as  being,  but  as  becoming.  Thus, 
"  A  cone  is  a  solid  generated  by  the  revolution  of  an  angle  about  one 
of  its  sides.7'  The  notion  defined  not  being  given,  but  made,  this  defi- 
nition is  synthetic. 

Logical  definitions  are  sometimes,  though  improperly,  called  defini- 
tions a  priori,  to  distinguish  them  from  definitions  a  posteriori.  A 
definition  a  posteriori  generalizes  the  conditions,  or  the  consequences 
of  a  concept,  or  explicates,  not  the  marks  connoted  but  the  things 
denoted.  E.  g.,  "  Malaria  is  that  which  induces  fever ;"  "  Mind  is  that 
which  knows  and  feels,  desires  and  wills."  Obviously  these  are  not 
definitions  at  all,  and  hence  are  also  called  pseudo-definitions.  The 
second  example,  which  merely  unfolds  the  denotation  of  mental  ac- 
tivity, is,  of  course,  strictly  a  logical  division. 

An  Explication,  unqualified,  evolves  only  some  of  the  marks.  An 
Exposition  is  a  series  of  explications.  A  Description  gives  marks  or 
characteristics  as  concrete  in  the  thing.  It  deals,  therefore,  only  with 
the  individual,  giving  any  number  of  its  marks,  the  selection  being 
governed  merely  by  the  purpose. 

§  5.  A  few  practical  RULES,  some  of  them  deduced  from  the  above 
principles,  and  useful  in  forming  good  definitions,  are  admissible  here. 
A  good  definition  must  be — 

1st.  Adequate.  If  the  genus  is  not  proximate,  the  definition  is  too 
wide.  If  the  difference  is  not  common  to  all  members  of  the  class, 
it  is  too  narrow.  E.  g.,  " Man  is  a  rational  being"  (too  wide) ;  or,  "is 
a  praying  animal "  (too  narrow).  A  convenient  test  of  adequacy  is 
convertibility  (§  1). 

2d.  Not  negative.  A  definition  ought  to  tell  what  a  thing  is,  but 
some  tell  merely  what  it  is  not.  E.  g.,  "  Parallels  are  lines  that  do  not 
meet ;"  "  Pleasure  is  the  feeling  opposed  to  pain."  Negative  state- 
ments serve  to  render  a  notion  clear,  and  are  valuable  as  precursory  to 
definition,  but  they  do  not  render  a  notion  distinct  (ii,  §  3).  If,  how- 
ever, the  notion  defined  is  essentially  negative,  as  shadow,  freedom, 
gentile,  want,  etc.,  then  its  definition  is  properly  negative.  E.  g.,  Cuvier, 
defined  an  invertebrate  as  "An  animal  destitute  of  an  internal  skeleton." 


DEFINITION.  ,          53 

3d.  Not  tautological.  A  definition  must  not  contain  the  name  of  the 
thing  defined,  nor  a  derivative  nor  a  synonymous  nor  a  correlative 
i  term,  for  this  is  to  define  a  thing  by  itself.  This  vice  is  called  defin- 
ing in  a  circle  or  reciprocally,  or,  by  the  ancients,  "  diallelon  "  (£m,  a\- 
X//Aa»').  It  is  a  sort  of  logical  seesaw.  E.  g.,  "  Life  is  the  sum  of  the 
vital  functions ;"  "  A  cause  is  the  concurrence  that  produces  an  ef- 
fect." Here  the  fault  is  immediate.  It  may  be  mediate.  E.  g.,  "  A 
board  is  a  thin  plank,"  and  "  A  plank  is  a  thin  board ;"  "  Law  is  the 
expressed  will  of  a  ruler,"  and  "A  ruler  is  one  who  gives  laws." 
There  is  a  similar  vice  in  reasoning,  called  by  the  same  names. 

4th.  Precise.  It  must  contain  nothing  unessential  or  superfluous. 
E.  g.,  "  Oats  is  a  grain  which  in  England  is  generally  given  to  horses, 
but  in  Scotland  supports  the  people"  (Dr.  Johnson).  This  specific 
difference  is  unessential.  So,  "  Man  is  a  risible  animal."  This  defi- 
nition does  not  fail,  nor  violate  strictly  logical  purity,  but  it  offends 
against  scientific  system  or  arrangement  of  thoughts.  Again,  "  A  tri- 
angle is  a  figure  having  three  sides  and  three  angles."  Here  is  super- 
fluity. Derivatives  should  be  excluded  as  superfluous,  for  they  are 
already  contained  in  their  originals.  E.  g.,  "  The  circumference  of  a 
circle  is  a  curved  line  returning  upon  itself,"  etc.  Every  line  return- 
ing upon  itself  is  a  curved  line ;  hence  "  curved  "  is  superfluous. 

5th.  Perspicuous.  It  should  be  intelligible,  literal,  and  brief.  We 
define  only  to  make  a  thought  more  distinct ;  hence  terms  more  con- 
fused than  the  one  defined  violate  perspicuity.  E.  g.,  "  Net-work  is 
anything  reticulated  or  decussated  at  equal  distances,  with  interstices 
between  the  intersections"  (Dr.  Johnson).  "The  soul  is  the  first  en- 
telechy  or  energy  of  a  natural  organized  body  possessing  life  poten- 
tially "  (Aristotle).  This  is  obscure,  says  Leibnitz.  Again,  all  figura- 
tive language  should  be  excluded.  Tropes,  for  instance,  do  not  indi- 
cate what  a  thing  is,  but  only  something  similar.  E.  g.,  "  The  Divine 
Nature  is  a  circle  whose  centre  is  everywhere  and  the  circumference 
nowhere."  Many  terms,  however,  originally  metaphorical  have  ceased 
to  be  so.  These  may  be  used,  and  sometimes  must  be,  especially  in 
mental  science.  Finally,  brevity  is  certainly  a  merit,  but  extreme  brev- 
ity may  leave  a  matter  more  obscure  than  needless  prolixity.3 


3  See  Hamilton's  Logic,  pp.  341-349.  His  treatment  is  borrowed  almost  entirely 
from  Krug,  Logic,  §§  121-123.  See  also  Mansel's  notes  in  Aldrich,  pp.  38-43,  and 
Appendix,  note  C.  Aristotle  discusses  Definition  in  Anal  Post.  bk.  ii.  See  espe- 
cially ch.  x.  ' 


54:  OF    CONCEPTS. 

§  6.  Praxis.     Analyze,  classify,  and  criticise  the  following : 

1.  A  line  is  length  without  breadth. — Euclid. 

2.  Science  is  classified  knowledge. 

3.  A  pump  is  a  machine  for  raising  water. 

4.  A  beggar  is  a  person  who  asks  alms. 

5.  Motion  is  the  translation  of  matter  through  space. 

6.  Words  are  signs  of  thoughts. 

V.  A  spheroid  is  formed  by  the  revolution  of  an  ellipse  about  its  di- 
ameter. 

8.  Philosophy  is  the  science  of  principles. 

9.  The  sun  is  the  orb  giving  the  light  of  day. 

10.  An  angle  is  the  inclination  of  two  lines  to  each  other. 

11.  Philosophy  is  the  recognition  of  mathematical  ideas  as  constitut- 

ing the  world. —  OJcen. 

12.  The  soul  is  the  principle  by  which  we  live,  feel,  move,  perceive, 

and  understand. — Aristotle. 

13.  Mind  is  spiritual  substance;  or,  is  the  conscious  subject. 

14.  Mind  is  the  unextended. — Bain. 

15.  Attention  is  consciousness  concentrated. 

16.  Perception  is  the  faculty  by  which  we  immediately  cognize  ex- 

ternal objects. 

17.  A  dragon  is  a  serpent  breathing  flame. 

18.  A  synopsis  is  a  conspectus  of  the  chief  points. 

19.  Logic  is  the  art  of  reasoning. 

20.  Logic  is  the  light-house  of  the  understanding  (pharus  intellectus). 

21.  A  pension  is  an  allowance  made  to  any  one  without  an  equivalent. 

In  England  it  is  generally  understood  to  mean  pay  given  to  a 
state-hireling  for  treason  to  his  country. — Dr.  Johnson. 

22.  Green  is  a  color  compounded  of  blue  and  yellow. 

23.  Dirt  is  matter  in  the  wrong  place. — Lord  Palmerston. 

24.  Truth  is  the  agreement  of  a  cognition  with  its  object. 

25.  A  spaniel  is  a  species  of  dog. 

26.  A  whale  is  a  fish  inhabiting  the  polar  seas,  and  furnishing  oil  as 

an  article  of  commerce. 

27.  Animal  is  the  genus  denoting  men,  beasts,  birds,  fish,  reptiles,  etc. 

28.  Wealth  is  things  useful,  necessary,  and  agreeable. 

29.  Pain  is  a  disagreeable  affection  of  mind  or  body. 

30.  A  feeling  is  a  mental  affection  involving  cither  pleasure  or  pain. 

31.  Beauty  is  the  feeling  we  experience  in  recognizing  unity  amidst 

variety. 


DEFINITION.  55 

32.  A  Sphinx  is  an  imaginary  monster  having  the  head  and  bust  of  a 

woman,  and  the  body  of  a  lion  with  wings. 

33.  A  circle  is  aline  returning  upon  itself,  all  the  points  of  which  are 

equidistant  from  a  given  point.4 

34.  A  triangle  is  a  figure  having  three  sides. 

35.  A  point  is  that  which  hath  no  parts  nor  magnitude. — Euclid. 

36.  A  fable  is  a  place  where  animals  talk  to  each  other,  which  .also 

they  do  not  do  so. — From  a  little  girVs  composition. 

37.  Man  is  the  star-gazing,  laughing,  food-cooking,  trading,  provident, 

instrument-using,  two-handed  biped. 

38.  Man  is  the  measure  of  the  universe. — Protagoras. 

39.  Man  is  the  featherless  biped. — Plato. 

40.  Common  salt  is  sodium  chloride;  or,  is  chloride  of  sodium. 

41.  An  elephant  is  an  animal  that  drinks  through  its  nostrils. 

42.  A  dog  is  a  digitigrade  quadruped,  having  fixed  claws,  four  toes, 

and  a  recurved  tail. 

43.  Excise:  a  hateful  tax  levied  upon  commodities,  and  adjudged  not 

by  the  common  judges  of  property,  but  by  wretches  hired  by 
those  to  whom  the  excise  is  paid. — Dr.  Johnson. 

44.  Honesty  is  integrity,  is  probity,  is  fair-dealing ;  or,  is  the  best  policy ; 

or,  is  uprightness  in  respect  to  transactions  relating  to  property. 

45.  Time  is  a  measured  portion  of  indefinite  duration. 

46.  Motion  is  the  act  of  potential  being  up  to  the  measure  of  its  po- 

tentiality.— Aristotle. 

47.  A  plane  triangle  is  a  figure  produced  by  a  plane  cutting  a  lim- 

ited cone  through  its  axis. 

48.  Virtue  is  a  voluntary  act  done  in  obedience  to  the  law  of  God. 

49.  Monarchy  is  a  form  of  political  government  in  which  one  man  is 

sovereign. 

50.  Capital  is  wealth  destined  to  consumption. 

51.  A  proposition  is  a  sentence  indicative. —  Whately. 

52.  Silence  is  the  entire  absence  of  sound  or  noise. 

53.  Health  is  the  condition  of  a  living  body  free  from  disease  or  pain. 

Define  the  following  terms,  both  really  and  genetically,  and  then 
consult  a  geometry : 

54.  A  line, — A  straight  line,— A  curved  line, — Parallel  lines, — An 

angle, — A  right  angle, — A  plane, — A  figure. 

4  Hamilton's  example  of  Real  Definition  (Logic,  p.  3-13). 


56  OF    CONCEPTS. 


VI.  DIVISION. 

§  1.  The  correlative  of  Definition  is  Division.  As  definition  relates 
primarily  to  the  intension,  or  depth,  of  a  concept,  so  division  relates 
primarily  to  its  extension,  or  breadth.  A  definition  explicates  or  evolves 
marks ;  a  division  explicates  or  evolves  subordinate  concepts  or  things. 
The  one  develops  the  comprehension ;  the  other,  the  sphere.  By  defi- 
nition the  connotation  is  analyzed ;  by  division,  the  denotation.  By 
definition  the  notion  is  rendered  internally  or  intensively  distinct ;  by 
division  the  notion  is  rendered  externally  or  extensively  distinct.  Thus 
the  notion  man  is  defined  by  unfolding  its  connoted  parts,  rational 
and  animal ;  it  is  divided  by  unfolding  its  denoted  parts,  as  logician 
and  non-logician.  Only  by  division,  says  Aristotle,  can  we  be  assured 
that  nothing  has  been  omitted  from  the  definition  of  a  thing. 

§  2.  As  preliminary,  it  is  needful  to  distinguish  two  kinds  of  wholes 
in  or  under  which  the  mind  thinks  the  objects  presented  to  it.  They 
are  as  follows : 

1st.  The  Logical  or  Qualitative  Whole.     This  is  of  two  sorts: 
(a.)  The  comprehensive,  characteristic,  or  intensive  whole,  whose 

parts  are  marks  evolved  by  Definition. 
(b.)  The  universal,  generic,  or  extensive  whole,  whose  parts  are 

species  or  things  evolved  by  Division. 

2d.  The  Mathematical  or  Quantitative  Whole.     Of  two  sorts : 
(a.)  The  integral  whole. 
(b.)  The  collective  whole.1 

The  logical  whole,  with  which  we  are  at  present  more  particularly 
concerned,  is  purely  subjective,  a  creation  of  thought.  It  is  qualita- 
tive ;  i.  e.,  it  is  the  concept  consisting  of  a  bundle  of  qualities  or  marks, 
and  containing  other  concepts.  These  its  parts  are  separable  only  by 
mental  abstraction.  There  are  two  species.  The  first,  the  intensive 
whole  (called  in  the  old  Logic  a  metaphysical  whole),  whose  parts  are 

1  Logic  commonly  distinguishes  also  the  Physical  Whole,  and  some  others ;  but 
we  shall  find  need  only  for  the  above.  See  Hamilton's  Logic,  pp.  142-144. 


DIVISION.  57 

marks,  has  been  considered  under  the  previous  topic.  The  second,  the 
extensive  whole,  whose  parts  are  kinds  or  things  unfolded  by  logical 
division,  is  more  especially  before  us. 

A  mathematical  whole  is  an  individual,  either  objective  or  subjec- 
tive, viewed  as  a  quantity,  and  consisting  of  parts  actually  separable. 
These  can  be  evolved  only  by  the  whole  being  cut  asunder,  i.  e.,  by 
partition,  which  must  be  clearly  distinguished  from  logical  division. 
Such  parts  are  neither  marks  nor  kinds.  This  whole  is  of  two  species. 
First,  the  integral  whole  is  one  in  which  its  parts  originate.  They 
may  be  homogeneous,  as  a  polygon  severed  into  similar  triangles;  or 
heterogeneous,  as  the  human  body,  consisting  of  head,  trunk,  and  limbs. 
Anatomy  is  a  science  of  partition,  of  dissection.  A  sword,  which  di- 
vides into  sabre,  rapier,  etc.,  is  parted  into  hilt  and  blade,  etc.  Sec- 
ondly, the  collective  whole  is  an  aggregation  of  similar  parts,  one 
originated  by  the  parts.  Such  are  the  notions  of  an  army,  a  forest,  a 
town.  These  are  formed  by  the  repetition  of  the  notions  of  a  soldier, 
a  tree,  a  house.  We  must  not  confound  the  notion  army,  which  is  a 
general  or  class  notion,  a  logical  whole,  with  the  notion  an  army 
taken  as  a  collective  notion,  an  individual  thing  formed  by  a  collection 
of  other  individual  things. 

§  3.  It  has  been  already  seen  how  by  specialization  we  form  sub- 
ordinate groups,  or  species.  Since  pure  Logic  considers  only  the  form, 
each  genus  or  universal  whole  can  contain  under  it  only  two  species, 
marked  with  A  and  non-A.  For  A  being  a  generic  difference,  i.  e.,  a 
mark  not  found  in  the  genus  or  divisum,  but  found  in  some  of  its 
members,  we  know  a  priori,  without  any  research  into  the  matter  of 
thought,  that  the  members  are  exclusive  of  each  other  and  exhaustive 
of  the  divisum.  This  is  division  by  dichotomy,  and  the  members  are 
contradictories.  For  illustration:  animals  are  rational  and  irrational, 
or  vertebrate  and  invertebrate  ;  angles  are  right  and  oblique  j  the  oblique 
are  acute  and  obtuse;  the  ancients  were  Greeks  and  barbarians,  or  Jews 
and  Gentiles,  or  bond  and  free.  The  process  viewed  intensive- 
ly, as  thinking  in  marks,  is  called  determination ;  viewed 
extensively,  as  establishing  species,  is  called  specification. 
In  relation  to  each  other,  the  two  species  are  co-ordinate,  as 
being  of  equal  rank  in  respect  of  the  divisnm ;  but  we  remark  that 
either  may  be  of  indefinitely  greater  breadth  than  the  other. 

The  negative  member  of  the  dichotomy  is  characterized  by  the  ab- 
sence of  the  mark  A,  or,  in  other  words,  by  the  negative  mark  non-A. 


58  OF    CONCEPTS. 

Hence  we  have  a  peculiar  class  of  concepts  called  negative,  privative, 
or  infinitated  concepts.  In  some  cases  their  sphere  is  very  wide,  de- 
noting almost  everything,  and  connoting  very  little,  almost  nothing 
positive.  E.  g.,  Ungodly,  unhappy,  apathy,  blindness,  senseless,  dark, 
cold,  infinite,  freedom,  shadow,  atheist,  idle,  sober,  dead,  etc. 

§  4.  When  the  process  is  pursued  beyond  a  single  division, — that 
is,  when  a  species  is  regarded  as  a  subaltern  genus  and  subdivided  into 
lower  species, — then  it  is  requisite  at  the  outset  to  select  some  one 
mark  of  the  original  divisum  as  a  ground  or  principle  on  or  in  ref- 
erence to  which  the  several  divisions  shall  be  made.  This  generic 
mark  so  chosen  is  called  the  ground  of  division,  fundamcntum  divi- 
sionis.  For  example,  in  dividing  Mankind  we  select  his  religious 
character  or  creed  as  the  ground  of  division,  and,  subdividing  upon 
the  same  principle,  we  obtain  a  logical  series,  thus : 

Mankind 

I 


Theists  Atheists 

I 

Monotheists  Polytheists 


Christians  Antichristians 


Papists  Protestants 


Jesuits  Non-Jesuits 

[etc.  etc.] 

The  number  of  distinct  forms  in  which  this  mark,  the  principle  of 
division,  appears  in  the  things  to  be  divided  will  determine  the  ex- 
tent of  the  series.  This  procedure  obviously  has  respect  to  the  matter 
of  thought,  and  is  not  strictly  pure  Logic.  We  add  that,  if  it  is  pro- 
posed to  establish  a  real  division,  i.  e.,  one  unfolding  the  true  nature  of 
the  things  contained  under  the  divisum,  or,  in  short,  one  rigidly  scien- 
tific, it  is  requisite  to  select  as  a  principle  of  division  an  essential  and 
original  mark  of  the  divisum,  and  to  adhere  to  it  throughout.  So 
logical  perfection  requires,  but  it  is,  in  fact,  rarely  practicable  in  an 
extended  series. 

And  this  suggests  that  the  distinction  made  between  nominal  and 
real  definition  may  well  be  carried  out  relative  to  division.  A  nominal 
or  artificial  division  would  be  one  made  for  some  transient  purpose 


DIVISION.  59 

or  to  attain  a  practical  end ;  or  one  tentative  and  precursory  to  a  real 
division ;  or  one  popularly  accepted  and  useful,  such  as  the  hundreds 
that  may  be  observed  on  every  page,  and  in  every  few  minutes  of" 
conversation.  A  real  or  scientific  division  would  be  one  proposing*  to 
divide  notions  and  things  according  to  their  true  and  essential  nature, 
in  order  to  attain  correct  objective  knowledge  of  things  as  they  are. 
Such  division  develops  natural  kinds,  and  is  to  be  looked  for  in  the 
more  refined  sciences.  The  Linna?an  artificial  divisions  of  flora  were 
precursory  and  tentative ;  those  of  Jussieu's  natural  system  are  real 
and  more  rigidly  scientific. 

§  5.  In  divisions  not  purely  logical,  but  having  respect  to  the  mat- 
ter, it  often  happens  that  we  have  those  more  than  dichotomous ;  we 
may  have  a  trichotomy  (rp/%a,  threefold ;  -ip>Eir,  to  cut),  or  a  po- 
lytomy.  E.  g.,  "Doctrines  are  helpful,  harmless,  hurtful."  This  arises 
from  two  causes.  Either  it  is  an  abbreviation  by  which  a  series  of 
subordinate  species  is  condensed  into  one  co-ordinate  statement,  as, 
"Angles  are  acute,  right,  and  obtuse ;"  or, " Mankind  are  Christians, 
Jews,  Mohammedans,  polytheists,  and  atheists ;"  or,  "  Plants  are  en- 
dogens,  exogens,  acrogens."  Or  it  arises  from  the  lack  of  a  sharp 
definition  of  our  concepts.  There  is  between  very  many  of  our 
thoughts  a  wide  border-land  which  it  is  impossible  to  assign  clearly 
to  either,  constituting  a  tertium  quid,  a  third  species  which  it  is  nec- 
essary to  insert  in  order  to  exhaust  the  divisum.  Thus  we  have  our 
twenty-four  hours  divided,  with  reference  to  their  light,  into  day,  twi- 
light, and  night.  So  we  have  "  White,  gray,  black  ;"  "  Riches,  com- 
petence, want ;"  "  Young,  middle-aged,  old,"  etc.  For  many  of  these 
mediate  species  we  have  no  names,  as  between  side  and  well ;  strong 
and  weak  ;  long  and  short ;  wise  and  foolish,  etc. 

We  have  remarked  that  in  a  strictly  logical  division  the  two  mem- 
bers, A  and  non-A,  are  contradictories ;  no  member  of  that  universe 
can  be  both,  nor  can  be  neither.  In  a  trichotomy  or  a  polytorny  the 
members  are  disparate  notions.  Thus,  brook,  creek,  river,  are  dis- 
parate notions  contained  under  the  genus  streams  of  water.  The 
two  extremes  of  such  a  division,  as  brook  and  river,  are  logical  con- 
traries. A  thing  of  this  genus  cannot  be  both,  but  may  be  neither ; 
it  may  be  the  tertium  quid. 

Let  it  be  also  noticed  that  in  many  cases  a  notion  which  seems  to 
have  been  originally  a  mere  negative  of  its  co-ordinate  notion  has  had 
thought  into  it  a  positive  character,  so  that  either  may  be  now  thought 


CO  OF    CONCEPTS. 

as  positive  and"  the  other  as  negative ;  or  perhaps  both  are  really  posi- 
tive, and  no  mere  negative  exists.  Thus,  white  and  black, — the  mere 
negative  is  dark.  So  true  and  untrue  or  false;  happy  and  unhappy  ; 
honor  and  dishonor  ;  temperate  and  intemperate,  which  last  has  become 
inverted.  So  protestant.  So  also  pleasure  and  pain.  Plato  taught 
that  pleasure  is  merely  the  absence  or  negation  of  pain ;  the  Hedo- 
nists taught  the  reverse ;  but  unquestionably  both  arc  positive.  Also, 
it  was  taught  anciently  that  evil  is  the  mere  negation  of  good ;  and 
to-day  there  are  those  who  hold  that  good  is  the  absence  of  evil ; 
but  both  good  and  evil  are  positive,  and  in  this  case  there  is  no  inter- 
mediate ground.  Actions  are  either  good  or  bad ;  there  are  no  indif- 
ferent actions. 

Finally,  a  polytomous  division  admits  of  one,  and  only  one,  strictly 
privative  or  negative  notion.  Thus,  **  Some  men  lend,  some  borrow, 
some  do  both,  others  do  neither;"  "Plants  are  monocotyledonous, 
dicotyledonous,  and  acotyledonous  or  flowerless."  The  intermediate 
ground,  well  named  the  undefined  or  indifferent  part,  often  takes  this 
negative  character ;  as  "  Men  are  very  industrious,  positively  lazy, 
and  neither  the  one  nor  the  other." 

§  6.  The  importance  of  the  correlative  processes  of  definition  and 
division  cannot  well  be  overrated.  They  are  the  reflex  respectively 
of  analysis  and  synthesis,  in  the  balance  of  which  lies  the  perfection 
of  knowledge.3  "  Such  is  the  excellency  of  definition  and  distribution," 
says  an  old  logician,  "  that  almost  they  alone  do  suffice  for  the  abso- 
lute putting-down  of  any  art ;  therefore,  the  wise  Socrates,  in  Phcedro 
Platonis,  saith  that  if  he  find  any  man  who  can  cunningly  divide,  he 
will  follow  his  steps  and  admire  him  for  a  god." 

We  shall  do  well,  then,  to  observe  the  following  practical  directions. 
From  the  account  given,  we  first  present  for  forming  divisions  this 
CANON  :  Assemble  representative  instances  of  the  objects  denoted 
by  the  divisum,  and,  having  fixed  upon  a  generic  mark  as  a  principle 
of  division,  select  a  mark  immediately  involving  this  principle  for  a 
specific  difference ;  then  divide  the  denotation  by  affirming  the  specific 
difference  of  the  species  which  it  determines,  denying  it  of  all  other 
contained  objects.  In  subsequent  divisions  pursue  a  similar  course, 

8  When  a  notion  is  adequately  defined,  and  thoroughly  divided,  we  have  attained 
a  complete  knowledge  of  its  characters  and  kinds,  and  this  process  exhausts  its 
content.  See  Kant's  Logik,  §  98. 


DIVISION.  61 

involving  in  each  new  specific  difference  the  one  immediately  preced- 
ing, and,  of  course,  the  original  principle  of  division. 

To  this  canon  we  now  append  the  following  RULES,  useful  as  a  fur- 
ther guide  to  correct  division : 

1st.  Each  division  throughout  a  series  should  be  governed  by  the 
same  principle,  which  should  be  an  essential  and  important  mark  of 
the  first  divisum. 

The  intervention  of  a  different  ground  of  division  in  the  series  gives 
rise  to  the  logical  fault  called  "Cross  division."  Thus:  "Men  are 
Europeans,  Americans,  negroes,  and  pagans."  This  is  an  abbreviated 
series  in  which  the  ground  of  the  first  division  is  geographical;  the 
second,  color ;  the  third,  religion.  The  members  evidently  cross  or 
overlap  each  other;  a  man  may  bo  all  of  the  last  three.  This  very 
common  vice,  when  more  concealed,  is  detected  and  the  division  tested 
by  dichotomy.  That  is  to  say,  any  trichotomy  or  polytomy,  if  cor- 
rect, may  be  reduced  to  a  dichotomy  by  taking  any  one  member  as 
positive  and  including  all  the  others  under  its  negative.  If  this  can 
be  done  with  each  member,  without  cutting  any  one,  the  division  is 
sound.  Thus,  "Physical  substance  is  animal,  vegetable,  mineral." 
Tested:  "P.  S.  is  A  and  non-A  (=V+M);"  or  is  "V  and  non-V 
(=A  +  M) ;"  or  is  "M  and  non-M  (=A+V)."  This  test  applied  to 
the  following  will  clearly  demonstrate  that  it  is  logically  vicious: 
"  The  religious  sects  of  Great  Britain  are  Catholic,  Calvinist,  Episco- 
pal, and  Dissenting." 

The  principle  selected  must  be  essential,  if  we  would  attain  to  real, 
scientific  knowledge.  It  must  be  important,  determining  many  other 
attributes,  if  we  would  evolve  an  extended  and  valuable  series.  The 
purpose  with  which  an  artificial  division  is  made  determines  its  ground. 
In  civil  affairs  it  would  be  useless  and  absurd  to  divide  men  into  horsemen 
and  footmen  ;  but  in  military  affairs  it  is  important.  Words  in  a  gram- 
mar are  divided  according  to  syntactical  relations ;  in  a  dictionary,  al- 
phabetically. Medical  botany  and  the  florist's  manual  will  divide  plants 
differently,  and  both  deviate  from  Jussieu.  We  sort  our  books  by  size,  to 
fit  our  shelves ;  by  subjects,  for  handy  reference ;  by  binding,  for  show. 

2d.  Dividing  members  must,  as  parts,  equal  the  whole  divisum. 

No  one  must  exhaust  the  divisum ;  as,  "  Mankind  are  rational  be- 
ings and  politicians."  Together  they  must  exhaust  it ;  as,  "  Govern- 
ments are  monarchies,  oligarchies,  and  democracies."  This  is  insuffi- 
cient ;  there  are  other  forms  of  government.  Together  they  must  not 
more  than  exhaust  it ;  as,  "  Vertebrates  are  quadrumana,  bimana,  quad- 


62  OF    CONCEPTS. 

rnpeds,  and  bipeds."  Bipeds  and  bimana  overlap  in  man.  Leibnitz 
calls  this  last  fault  "  communicant  species."  So,  "  Imaginative  writers 
are  poets,  dramatists,  and  writers  of  tales."  Again,  "  Sciences  are  de- 
ductive and  inductive."  These  species  are  communicant,  since  the  lat- 
ter makes  large  use  of  deduction.  There  is  no  science  non-deductive. 

3d.  Divisio  ne  faciat  sal  turn. 

Each  species  must  emerge  directly  from  its  own  proximate  genus. 
Thought  must  not  overlook  and  overleap  its  immediate  parts  and 
spring  from  the  divisum  to  remote  species.  This  the  theory  requires ; 
but  practically,  for  the  sake  of  brevity,  such  a  saltus  is  allowed, 
thought  passing  through  intermediate  steps  to  guard  against  error. 
Thus  we  may  say  that  "Mathematics  treats  of  infinitesimals,  as  well  as 
of  magnitudes  of  assignable  quantity."  This  last  member  equals  "  non- 
infinitesimals."  The  genus  "mathematical  subjects"  is  far  from  being 
proximate  to  these  species.2 

§  7.  Praxis.  Are  the  following  sixteen  examples  Partitions  or 
Divisions,  or  neither?  If  Divisions,  are  they  correct?  If  not,  point 
out  the  defects.  If  correct,  reduce  to  dichotomous  statement. 

1.  Propositions  are  affirmative,  hypothetical,  and  negative. 

2.  Thought  is  by  conception,  or  by  judgment,  or  by  reasoning. 

3.  The  mental  faculties  are  sensation,  perception,  imagination,  mem- 

ory, and  judgment. 

4.  Is  the  year  or  are  the  seasons  divided  into  spring,  summer,  au- 

tumn, and  winter  ? 

5.  A  flower  consists  of  calyx,  corolla,  stamens,  and  pistil;  and  the 

pistil  consists  of  ovary,  style,  and  stigma. 

6.  Literature  consists  of  writings  historical,  religious,  poetical,  clas- 

sical, and  current. 

7.  Matter  is  solid,  liquid,  and  aeriform.     What  is  the  principle  ? 

8.  Languages  are  Aryan,  Semitic,  and  Turanian. 

9.  Rectilineal   figures   are  triangles,  rectangles,  parallelograms,  and 

figures  of  more  than  four  sides. 

2  See  Hamilton's  Logic,  Lect.  xxv.  His  doctrine  is  drawn  mostly  from  Esser's 
Logic,  §§  134-137.  See  also  Thomson's  Outline,  §  55 ;  and  Drobisch's  Logic, 
§  119.  Division  was  a  favorite  method  with  Plato  for  the  demonstration  of  Defi- 
nitions, which  Aristotle  censures  (Anal.  Post.  bk.  ii,  ch.  v),  and  teaches  that  its 
chief  use  is  to  test  definitions  when  obtained.  Among  the  later  Peripatetics  the 
method  was  more  esteemed.  Modern  logicians  have  drawn  chiefly  from  Bcethius's 
work  De  Divisione.  Cf.  Cic.  Top.  ch.  vi,  and  Quintil.  v,  10.  See  also  Kant's  Logic, 
§  113;  and  Trend,  Elem.  §  58. 


DIVISION.  Go 

10.  The  Federal  domain  consists  of  states  and  territories ;  the  states,  of 

Northern,  Southern,  etc. ;  and  each  state  is  divided  into  counties. 

11.  The  elements  of  a  true  civilization  are,  a  wise  and  just  polity,  a 

general  intelligence,  and  an  aesthetic  culture. 

12.  Job's  family  contained  sons  and  daughters.     Job's  children  were 

sons  and  daughters.     The  sons  of  Zebedee  were  James  and  John. 

13.  The    fine    arts    are    drawing,    painting,    sculpture,    architecture, 

poetry T  and  photography. 

14.  Wealth  naturally  divides  itself  into  three  portions — 1st.  That 

which  is  reserved  for  immediate  consumption,  and  of  which  the 
characteristic  is  that  it  affords  no  revenue  or  profit;  2d.  The 
fixed  capita],  which  affords  profit  without  circulating  or  changing 
masters ;  3d.  The  circulating  capital,  which  affords  a  profit  only 
by  circulating. — A.  Smith. 

15.  Profits  are  divided  into  interest,  insurance,  and  wages  of  superin- 

tendence.— Mill. 

16.  The  origin  of  colonies  is  to  be  traced  either  to  the  necessity  for 

frontier  garrisons,  as  among  the  Romans,  or  to  the  poverty  or  dis- 
content of  the  inhabitants  of  the  mother-country,  as  among  the 
Greeks. 

17.  Divide  and  subdivide  Triangle  so  as  to  include  the  scalene,  the 

right-angled,  the  equiangular,  the  obtuse-angled,  and  the  isosceles. 

18.  Make  several  divisions  of  Citizens,  stating  the  principle  in  each, 

into  these  given  species :  Laity,  aliens,  naturalized,  peers,  clergy, 
baronets,  native,  commons. 

19.  Divide  Man  on  the  principle  of  age,  sex,  family  relations,  color, 

stature,  riches,  rank,  education,  occupation,  and  disposition. 

20.  Are  Books  or  is  A  Library  divided  into  folios,  quartos,  octavos, 

and  duodecimos  ? 

21.  Is  the  distinction  of  The  Ten  Virgins  into  five  wise  and  five  fool- 

ish a  logical  division  or  a  partition  ? 

22.  Divide  and  subdivide  the  Officers  of  the  United  States  Govern- 

ment with  reference  to  their  official  functions. 

23.  Divide  and  subdivide  War  on  any  designated  principle. 

24.  Divide  and  subdivide  Pleasures  on  the  ground  of  their  effect  on 

the  mind  and  character. 

25.  Give  the  divisions  and  subdivisions  of  Topic  iv,  on  Relation. 

26.  Reduce  the  definitions  in  v,  §  2,  to  dichotomous  divisions. 

27.  Reduce  the  divisions  in  vi,  §  4,  to  a  series  of  definitions. 

28.  Reduce  the  definitions  in  vii,  §  6,  to  dichotomous  divisions. 


64  OF    CONCEPTS. 


VII.  COMPLETE  SYSTEM. 

§  1.  In  concluding  this  general  division  of  Logic  treating  of  the 
Concept,  it  is  needful  to  gather  up  into  one  some  of  the  results  ob- 
tained, and  this  will  give  occasion  to  remark  a  few  additional  points. 
The  notion  of  a  series  of  related  concepts  has  been  anticipated,  es- 
pecially under  the  last  topic.  We  proceed  to  examine  the  form  of 
such  a  series  when  it  is  evolved  into  a  complete  system. 

As  preliminary,  and  at  the  risk  of  some  repetition,  we  will  present 
and  remark  upon  the  following  scheme  of  the  two  quantities : 

£i  f  Existing Minerals,  Plants,  Brutes,  Men.  ~j  p 

g  I  Existing,  living Plants,  Brutes,  Men.   I  •§ 

2.  j  Existing,  living,  sentient Brutes,  Men.   j  % 

?  i.  Existing,  living,  sentient,  rational Men.  j  w 

The  most  obvious  point  here  illustrated  is  the  law  of  thought  that 
as  intension  increases,  extension  diminishes,  and  vice  versa  ;  that  the 
maximum  of  either  one  is  the  minimum  of  the  other ;  that  these  two 
quantities  of  thought  are  in  inverse  ratio. 

In  ascending  the  series  we  think  out  marks  and  think  in  things  in 
the  same  act.  For  each  mark  thrown  out,  a  concept  is  brought  in. 
Now  this  act,  on  the  intensive  side,  this  thinking  out  marks,  is  ab- 
straction ;  for  in  it  we  draw  away  a  complement  of  marks,  and  thus 
abstract  these  from  at  least  one  other  which  passes  out  of  conscious- 
ness. Thus,  we  first  abstract  existing,  living,  sentient,  from  rational  • 
then  existing,  living,  from  sentient ;  then  existing  from  living.  On 
the  side  of  extension  there  is,  for  each  abstraction,  a  generalization. 
In  thinking  out  rational,  we  think  in  brntes,  i.  e.,  the  marks  existing, 
living,  sentient,  are  generalized  as  belonging  to  brutes  in  common 
with  men;  and  these  two  classes  of  things  are  united  in  the  more 
general  or  generic  class  which  we  term  animal.  Hence,  generalization 
is  also  generification.  It  follows  that  abstraction  and  generalization 
are  what  might  be  called  directly  parallel  correlatives ;  directly  parallel, 
as  moving  in  the  same  direction  in  the  different  quantities. 

In  descending  the  series,  we  think  in  marks  and  think  out  things 
in  the  same  act.  This  act,  on  the  intensive  side,  is  determination, 


COMPLETE    SYSTEM.  05 

because  the  bringing  in  a  mark,  while  it  narrows  down  and  fixes  spe- 
cifically or  definitely  the  limit  of  a  smaller  class  of  things,  also  at- 
tains a  fuller,  deeper  knowledge  of  them.  Determination,, which  in 
the  scheme  descends,  is  the  inverse  correlative  of  abstraction,  which 
ascends.  On  the  side  of  extension,  there  is  for  each  determination  a 
specialization.  In  thinking  in  sentient,  into  existing,  living,  we  think 
out  plants,  i.  c.,  the  notion  organism  is  specialized  into  animal  by 
excluding  vegetation,  and  we  have  established  a  subordinate,  special, 
or  specific  class,  animal.  Hence  specialization  is  also  specification. 
Specialization,  which  descends,  is  the  inverse  correlative  of  generaliza- 
tion, which  ascends.  Finally,  determination  and  specialization  may 
also  be  called  directly  parallel,  or,  simply,  parallel  correlatives. 

It  should  also  be  observed  that  on  the  one  side  abstraction  is  analy- 
sis, and  determination  synthesis ;  while,  on  the  other  side,  the  order  is 
reversed,  specialization  is  analysis,  and  generalization  is  synthesis. 
Hence  the  movement  that  is  analysis  in  one  quantity  of  thought,  is 
synthesis  in  the  other.  The  neglect  of  this  distinction  by  logical 
authors  has  led  to  much  confusion  in  the  use  of  these  terms. 


§  2.  The  isagogue  of  Porphyry  to  the  Categories  of  Aristotle,  writ- 
ten in  the  third  century,  was  designed  as  a  detailed  explanation  of  the 
relations  of  genera  and  species.  From  its  doctrine  subsequent  logi- 
cians constructed  a  scheme  which,  because  of  the  form  it  presented, 
was  called  by  the  Latins  the  tree  of  Porphyry  (arbor  Porpyriana), 
and  by  the  Greeks  the  ladder  (xA/juaQ.1  It  exhibits  a  hierarchy  of  con- 
cepts representing  a  complete  system.  The  following  scheme  presents 
the  device  in  a  modified  form,  with  the  same  matter  already  used: 


Second  Intentions.  . 
Concepts  of  Concepts. 

First  Intentions. 
Concepts  of  Things. 

Intension  or  Depth. 
Marks  connoted. 

Extension  or 
Breadth. 
Things  denoted. 

Summum  Genus 
Species  or  Sub-genus 
Species  or  Sub-genus 
Iiifima  Species 

Individual 

Being  or  Thing 
Organism 
Animal 
Man 

Aristotle 

Existing 
Ex.,  Living 
Ex.,  Lv.,  Sentient 
Ex.,  Lv.,  Sn.,  "Eational 

Ditto  and  Father  of  Logic- 

All  Things 
All  Organisms 
All  Animals 
All  Men 

One  Being 

1  For  a  delineation  of  it,  as  given  by  Thomas  Aquinas,  see  Mansel's  Aldrich,  p. 
32.  The  isagogue  will  be  found  appended  to  Owen's  translation  of  the  Organon 
of  Aristotle  (Bonn's  ed.) ;  and  also  prefixed  to  St.  Hilaire's  Logique  D'Aristote, 
traduite  (Paris,  1844).  The  doctrine  of  the  isagogue  is  drawn  largely  from  the 
writings,  and  sometimes  is  expressed  in  almost  the  very  words,  of  Plato. 

5 


66  OF    CONCEPTS. 

§  3.  It  is  evident  that  the  mind,  rising  from  individuals  to  classes, 
and  by  successive  generalizations  forming  wider  and  wider  classes  or 
genera,  at  each  step  diminishing  the  marks  connoted,  at  last  must 
reach  a  notion  of  widest  generality,  connoting  but  one  mark,  above 
which,  of  course,  it  cannot  rise ;  and  the  process  necessarily  ceases. 
This  highest,  widest  notion  is  called  the  "  summum  genus,"  and  is  de- 
fined as  the  genus  that  cannot  become  a  species.  It  is  represented 
in  the  above  scheme  by  Being  or  Thing,  containing  in  it  only  the  no- 
tion existing,  and  containing  under  it  all  things.  This  is  a  simple 
notion  and  cannot  be  defined,  not  being  referable  to  a  genus. 

The  Aristotelian  logicians  consider  the  summa  genera  as  fixed  by 
nature,  and  ten  in  number,  corresponding  to  the  ten  Categories  or 
Predicaments  of  Aristotle.2  By  the  Categories,  Aristotle  means,  meta- 
physically, a  classification  a  posteriori  of  the  modes  of  objective  or  real 
existence;  logically,  a  classification  of  the  most  general  terms  that 
can  be  predicated  of  any  subject  whatever.  They  are  as  follows,  illus- 
trated by  his  own  examples : 

1.  Substance; — it  is  a  man,  a  horse,  etc. 

2.  Quantity ; — it  is  two  cubits  long,  three  cubits,  etc. 

3.  Quality ; — it  is  white,  grammatical,  etc. 

4.  Relation ; — it  is  double,  half  as  large,  greater,  etc. 

5.  Action  ; — it  cuts,  burns,  etc. 

6.  Passion ; — it  is  cut,  is  burned,  etc. 

7.  Place ; — it  is  in  the  Agora,  in  the  Lyceum,  etc. 

8.  Time; — it  is  to-day,  was  yesterday, last  year,  etc. 

9.  Posture ; — it  is  recliningj  seated,  etc, 

10.  Possession  ; — it  is  having  shoes,  armor,  etc. 
Everything  that  can  be  spoken  of  or  thought  of  comes  under  one 
or  the  other  of  these  Categories ;  in  other  words,  whatever  can  be  a 
subject  of  predication  is  in  one  or  the  other  of  these  Predicaments. 
Each  is,  therefore,  the  highest  generalization  of  a  series  of  notions, 
each  a  summum  genus.  Aristotle,  in  his  logical  writings,  whatever 
place  they  may  hold  in  his  metaphysics,  evidently  intends  the  Catego- 
ries to  be  an  enumeration  of  the  widest  notions  signified  by  single 
terms.  They  have  excited  a  world  of  discussion,  been  sharply  criti- 
cised, banished  repeatedly  to  metaphysics,  and  as  often  recalled  to 
Logic.  Kant  objects  to  them :  1st.  That  the  analysis  is  not  made 
on  any  one  principle ;  2d.  That  the  enumeration  is  incomplete ;  3d. 

8  Categories,  ch.  iy.     See  also  Topica,  \,  9  ;  and  Metaphysica,  iv,  7. 


COMPLETE    SYSTEM. 


That  empirical  notions  are  intruded  among  the  pure,  and  derivative 
among  the  original.     Hamilton  objects  that  the  summum  genus  of 
each  series  is  not  absolute,  but  included  under  one  higher.3 
lie  redistributes  the  series  thus : 


Being,  ens.  - 


Per  se,  i.  e.,  Substance,  substantia,  (1). 

f    Absolute       ,     Matter,  gwontfto,  (2). 
(     Form,  qualitas,  (3). 

Per  accidens, 
i.  e.,  mode  of 
substance. 

Relative, 
relatio,  (4). 

r   Action  and  Passion, 
aclio  et  passio,  (5  and  6). 
Place,  ubi,  (7). 
Time,  quando,  (8). 
Posture,  situs,  (9). 
L    Possession,  habitus,  (10). 

Practically,  particular  sum  ma  genera  are  assumed  in  different  de- 
partments of  thought.  Usually,  that  notion  is  accounted  the  sumnium 
genus  which  is  characterized  by  the  mark  selected  as  the  principle  or 
ground  of  the  division.  This  summum  genus  is  the  subject  of  the 
science.  Thus,  in  botanical  science,  "  Plant"  will  be  the  actual  sum- 
mum  genus ;  in  zoology,  "  Animal ;"  in  chemistry,  "  Compound  sub- 
stance," in  political  economy,  "Wealth ;"  and  so  in  more  common- 

8  See  Logic,  pp.  139-141 ;  and  his  note  in  Reid's  Works,  p.  687.  See  also  Kant's 
Kritik  der  r.  V.  p.  65 ;  Mill's  Logic,  p.  45  sq. ;  and  Hansel's  Aldrich,  Appendix, 
Note  B.  For  historical  matter,  see  Trendelenburg's  Gcschichte  der  KatcgorienleKre. 

A  popular,  concrete  illustration  of  the  Categories  was  given  by  Cornelius  to  his 
pupil  in  Martinus  Scriblerus,  which,  as  a  mnemonic,  we  quote  as  follows : 

"  Cornelius  was  forced  to  give  Martin  sensible  images.  So,  calling  up  £he  coach- 
man, he  asked  him  what  he  had  seen  at  the  bear-garden.  The  man  answered :  I 
saw  two  men  fight  for  a  prize ;  one  was  a  fair  man,  a  sergeant  in  the  guards,  the 
other  black,  a  butcher ;  the  sergeant  had  red  breeches,  the  butcher  blue ;  they 
fought  on  a  stage  about  four  o'clock ;  and  the  sergeant  wounded  the  butcher  in 
the  leg.  Mark,  quoth  Cornelius,  how  the  fellow  runs  through  the  Predicaments : 
Men  (substantia},  two  (quantitas),  fair  and  black  (qualitas),  sergeant  and  butcher 
(relatio),  wounded  the  other  (actio  et  passio),  on  a  stage  (ubi),  four  o'clock  (quando), 
fighting  (situs),  blue  and  red  breeches  (Jtabitus)" 

Another  mnemonic  is  as  follows : 

124  3  5  6 

Arbor  sex  servos  fervore  refrigerat  ustos, 

789  10 

Ruri  eras  stabo,  nee  tunicatus  ero. 

These  two  mnemonics  will  also  serve  to  illustrate  the  statement  that  Logic  is  an 
analysis  not  merely  of  scientific,  but  of  the  most  common-place  thinking. 


68  OF    CONCEPTS. 

place  matters.  See  example  invi,  §4,  where  "Mankind"  is  the  sum- 
mum  genus.  But  the  frequent  use  of  the  words  "  thing,"  "  being," 
etc.,  shows  what  constant  mental  reference  is  had  to  the  true  sum- 
mum  genus.  Indeed,  whenever  we  do  not  know  the  proximate  or  an 
approximate  genus  of  an  object,  or  do  not  care  to  be  exact,  we  mount 
up  on  eagles'  wings,  and  call  it  "  a  thing."  Thus :  "  A  comet  is  a 
curious  thing."  Also,  whenever  we  wish  to  consider  an  object  relative 
to  some  one  mark  especially,  or  exclusively,  we  call  it  a  thing,  thus 
omitting  all  others  by  a  direct  reference  of  it  to  the  summum  genus ; 
as,  "  Wine  is  a  hurtful  thing,  because,"  etc.  So,  also,  when  we  wish 
to  emphasize  some  one  mark  ;  as,  "  Cruelty  is  a  hateful  thing." 

§  4.  On  the  other  hand,  when  the  mind  descends  in  thought,  add- 
ing marks  and  rejecting  things,  it  must  finally  reach  a  class  of  things 
that  contains  under  it  only  individuals,  a  class  that  connotes  a  maxi- 
mum plurality  of  common  marks,  and  denotes  a  minimum  plurality 
of  things.  Here  the  process  of  logical  division  into  kinds  must  cease. 
This  deepest,  narrowest  class  is  called  the  "  infima  species ;"  and  is  de- 
fined as  the  species  that  cannot  become  a  genus.  It  is  represented  in 
the  scheme  by  Man,  containing  in  it  many  common  marks,  and  con- 
taining under  it  only  individual  human  beings. 

The  Aristotelic  logicians  consider  the  infima  species  also  as  fixed 
by  nature,  and  expressed  in  terms  like  man,  horse,  etc.  Classes,  such 
as  negroes,  mustangs,  etc.,  would  not,  by  them,  be  admitted  to  be 
species  at  all,  but  only  accidental  varieties.  But  the  whole  question 
of  natural  kinds  belongs  entirely  to  the  naturalist,  and  with  it  Logic 
has  nothing  to  do.  Pure  Logic  cannot  discriminate  between  essential 
and  accidental  marks.  The  logician  gets  nothing  from  objective  nature 
but  individuals,  and  elaborates  from  them  his  system  without  any  other 
restriction  than  the  primary  laws  of  thought.  Hence  the  division 
into  logical  kinds  continues  until  no  mark,  common  to  even  two  in- 
dividuals, remains.  The  species  that  comprehends  all  the  common 
marks  is  theoretically  the  infima  species,  for  that  only  cannot  be  made 
a  genus  by  further  division. 

The  individual  then,  not  being  a  kind,  is  not  a  logical  part,  i.  e.,  can- 
not be  obtained  by  division.  The  constituents  of  the  infima  species 
may,  however,  be  estimated  numerically,  may  be  counted,  and  hence 
it  is  spoken  of  as  containing  under  it  individuals.  But  the  individual, 
as  the  word  indicates,  is  also  described  as  that  which  cannot  be  divided. 
What,  then,  is  the  difference  by  which  to  distinguish  the  individual 


-*.^ 

COMPLETE    SYSTEM.  ^^^Ss  69 


from  the  infima  species  ?  It  is  that,  while  the  infima  species  consists 
only  of  common  marks,  the  individual  possesses,  besides  these,  at  least 
one  particular  mark,  represented  in  the  scheme  by  Father  of  Logic. 
This  particular  mark  determines  only  a  numerical,  and  not  a  specific 
difference  ;  therefore,  the  individual  cannot  be  defined,  but  only  de- 
scribed.  Such  is  the  logical  individual.  The  actual,  or  real,  individ- 
ual possesses  also  a  distinct  existence  in  space  or  time.  It  can  be  sev- 
ered only  by  partition,  and  can  be  discriminated  only  in  perception, 
external  or  internal.  Its  numerical  differences  are  endless. 

§  5.  The  scheme  before  us  is  obviously  very  meagre  and  brief,  pre- 
senting no  more  than  is  requisite  to  exemplify  the  principles  of  classi- 
fication. The  extent  of  any  series  is,  theoretically,  incalculable,  but 
practically,  and  in  view  of  the  matter  of  thought,  the  upper  and  lower 
limits  are  soon  reached.  If  the  characters  which  afford  the  principle 
of  such  a  division  are  only  external  and  contingent,  there  is  a  division 
in  the.  wider  sense;  if  they  are  internal  and  constant,  there  is  a  divi- 
sion in  a  stricter  sense  ;  if  they  are  not  only  internal,  but  also  essential 
and  original,  there  is  a  division  in  the  strictest  sense.  Starting  with 
any  assumed  summum  genus,  even  the  wider  divisions  must  soon  prac- 
tically terminate  in  an  infima  species,  though  the  strictest  divisions,  as 
in  the  botanical  natural  system,  may,  treated  by  dichotomy,  extend 
through  some  hundreds  of  steps.  But  pure  Logic  takes  no  account  of 
characters  as  accidental  or  essential,  as  congruent  or  repugnant.  As 
far  as  the  laws  of  thought  are  concerned,  it  is  permitted  to  unite,  in 
an  act  of  conception,  any  attributes  which  are  not  contradictory  of 
each  other.  The  number  of  attributes  in  the  universe  not  thus  logi- 
cally incompatible  with  each  other,  is  infinite,  and  the  mind,  therefore, 
finds  no  limit  to  its  downward  progress  in  the  formation  of  subordi- 
nate notions. 

Hence,  theoretically,  the  summum  genus  and  the  infima  species  are 
both  unattainable  except  per  saltum.  We  may  approximate,  but  never 
reach  them.  This  impossibility  is  expressed  in  two  laws,  as  follows  : 

1st.  The  law  of  homogeneity  :  —  Any  two  notions  the  most  dissimi- 
lar must,  in  some  respect,  be  similar.  Consequently  they  can  always 
be  subordinated  to  some  higher  concept. 

2d.  The  law  of  heterogeneity:  —  Any  two  notions  the  most  similar 
must,  in  some  respect,  be  dissimilar.  This  dissimilarity  furnishes  the 
ground  for  a  new  division,  which  process,  therefore,  may  be  continued 
ad  infinitum. 


70  OF    CONCEPTS. 

§  6.  Before  dismissing  the  tree  of  Porphyry,  attention  must  be  re- 
called to  the  relations  of  definition  and  division.  Definition  looks  up 
the  scale ;  division,  down.  When  a  subject  is  to  be  fully  treated,  we 
first  define  it.  We  give  the  specific  difference,  which  sets  it  apart 
from  co-ordinate  notions,  and  then  the  proximate  genus,  the  one  next 
above,  which  involves  all  the  marks  of  the  preceding  genera,  including 
the  highest.  Thus  the  definition  comprises  all  the  scale  lying  above 
its  subject.  Next  we  proceed  to  divide  and  subdivide  until  we  reach 
and  include  the  lowest  species.  Thus  division,  moving  downward,  ex- 
hausts the  scale.  The  system  then  is  complete,  the  work  is  thorough- 
ly done,  the  treatment  is  scientifically  expansive  and  exhaustive. 

It  is  not  necessary  that  this  order  should  be  rigidly  observed.  In 
the  progress  of  a  treatise  the  form  of  definition  may  often  replace  di- 
vision, and  one  or  the  other  will  preponderate  according  to  the  point 
in  the  scale  at  which  a  beginning  is  made,  or  according  to  the  inclina- 
tion of  the  writer  or  the  nature  of  the  subject.  In  Plato's  Kepublic, 
one  of  the  noblest  examples  of  logical  method,  successive  definitions 
of  justice  are  brought  to  the  test  and  rejected  until  a  satisfactory  one 
is  obtained.  Then  division  preponderates,  in  the  enumeration  of  the 
powers  of  the  human  soul,  and  of  the  classes  in  a  State  that  answers 
to  them  ;  as  well  as  of  the  declinations  through  which  the  perfect  pol- 
ity, if  it  could  be  constructed,  would  have  to  pass.  The  whole  is 
fused  together  and  adorned  by  a  dramatic  element,  in  such  a  manner 
as  to  render  this  dialogue  the  finest  work  of  heathen  philosophy.  In 
the  Nicomachean  Ethics  of  Aristotle,  definition  predominates,  but  with 
considerable  aid  from  division.  Thus  he  enumerates  the  opinions  of 
men  about  "  the  good,"  and  rejects  all  but  the  right  one.  Defining 
that  under  the  name  of  "  happiness,"  he  is  led  on  to  define  the  parts 
of  his  first  definition ;  and,  in  the  case  of  the  moral  and  intellectual 
virtues,  he  does  not  consider  his  explanation  complete  without  a  di- 
vision of  both  classes.4 

Since  definition  and  division  are  convertible  correlatives,  a  scientific 
system  may  be  expressed  entirely  either  in  tabulated  divisions,  or  in  a 
series  of  definitions.  These  are,  mutatis  mutandis,  the  same  thing. 
We  may  begin  with  the  summum  genus,  and,  descending,  exhaust  the 
scale  by  a  series  of  divisions.  Or,  we  may  begin  with  the  infima 
species,  and,  ascending,  exhaust  the  scale  with  a  series  of  definitions. 
Any  specific  concept  being  defined,  it  is  requisite  to  define  the  proxi- 

4  See  Thomson's  Outline^  §  128. 


COMPLETE    SYSTEM.  71 

mate  genus  to  which  it  is  referred,  and  again  the  proximate  genus  to 
which  this  is  referred,  and  so  on,  until  the  summum  genus  is  reached ; 
whence  a  series,  a  complete  system.  As  a  crude  illustration,  we  give 
from  Political  Economy  the  following : 

Wages  is  circulating  capital  paid  in  remuneration  of  labor. 
Circulating  capital  is  capital  consumed  in  a  single  use. 
Capital  is  wealth  destined  to  reproductive  consumption. 

Wealth  is  things  useful  or  agreeable,  which  cannot  be  obtained  without  labor  or 
sacrifice. 

This  series  is  readily  convertible  into  divisions;  and,  to  speak  gener- 
ally, definitions  and  divisions  are  mutually  convertible. 

Certain  sciences,  as  Botany  and  Zoology,  are  sometimes  called  the 
classificatory  sciences,  because  they  exhibit  their  matter  mostly  in  the 
form  of  divisions.  But  all  sciences  are  classificatory,  and  those  re- 
ferred to  should  rather  be  called  the  dividing  sciences,  in  opposition 
to  defining  sciences,  such  as  exhibit  their  matter  mostly  in  the  form 
of  definitions.  Chemistry,  for  example,  is  eminently  a  defining  science. 
It  exhibits  very  few  divisions.  Having  named  the  elements,  it  em- 
ploys hardly  any  other  technical  names,  a  compound  substance  being 
known  generally  only  by  its  definition,  which  takes  the  place,  of  a 
name,  as  "Potassium  iodide,"  "Nitrate  of  cupric  oxide,"  etc.  It 
would  be  quite  possible  to  state  the  relations  of  chemical  substances 
as  genera  and  species. 

§  7.  It  is  thus,  in  the  manner  and  with  the  formal  results  which 
have  now  been  described,  that  we  do  think,  and,  governed  by  the  nec- 
essary laws  of  pure  thought,  it  is  thus  that  we  must  think.  Our 
thoughts  are  elaborated  and  rendered  distinct  by  being  co-ordinated 
and  subordinated,  by  being  divided  and  defined,  until  they  are  gradu- 
ally built  up  into  systems  more  or  less  imperfect,  more  or  less  incom- 
plete. And,  be  it  observed  again,  this  is  the  case  not  merely  in  refined 
science,  but  is  equally  true  of  our  every-day  thinking,  and  that  about 
the  most  trivial  matters.  The  difference  is  not  in  kind,  but  in  degree, 
the  common-place  thinking  being  only  more  multifarious  and  imper- 
fect. Every  common  noun  in  language  occupies  a  place  in  some  one 
of  the  countless  hierarchies  of  concepts  which  the  human  mind,  for 
various  purposes,  has  been  led  to  form.  Nay,  far  more  than  that, 
every  common  noun  is  the  point  of  intersection  of  a  multitude  of 
linear  systems  crossing  each  other  at  all  possible  angles,  and  inter- 
weaving with  each  other,  so  that  each  occupies  a  place,  not  merely 


OF    CONCEPTS. 


in  one,  but  in  many  series.  It  is  true  that  in  most  minds  there  is 
much  confusion  and  disorder  in  this  fabric  of  thought,  an  entangling 
evinced  by  the  indefinite  and  very  ambiguous  character  of  common 
words.  Still,  the  greater  part  of  the  humblest  mental  life  is  occupied 
in  generalizing  and  specializing,  in  systematically  arranging  and  cor- 
recting the  arrangement  of  thoughts. 

When  Captain  Cook  landed  a  cow  in  the  South  Sea  Islands,  the 
savage  natives  exclaimed  in  astonishment :  It  is  a  kind  of  goat !  The 
goat  being  the  only  horned  animal  known  to  them,  they  generalized 
this  mark.  They  specialized  by  thinking  in  the  difference  large ;  so 
their  definition  was :  A  cow  is  a  large  goat.  It  may  be  hoped  that 
they  have  now  corrected  the  matter  of  this  classification,  but  in 
form  their  logic  was  at  once  perfect.  If  I  should  speak  of  a  button, 
a  child  might  ask:  What  do  you  mean  by  button?  It  being  by  no 
means  easy  to  define  this  familiar  thing,  I  may  escape,  and  satisfy  the 
querist  by  naming  and  describing  the  different  kinds  of  buttons ;  or, 
perhaps  more  easily  still,  show  it  a  specimen,  saying :  This  is  a  button, 
— which  will  do  pretty  well,  since,  according  to  the  scholastic  aphorism, 
omnis  intuitiva  notitia  est  definitio.  This  is  more  easy,  for  in  it  I  de- 
cline to  think  the  matter,  and  throw  the  burden  of  thinking  it  on  the 
child.  Every  book,  whose  author  has  well  digested  his  subject,  illus- 
trates the  point.  In  turning  the  leaves,  we  find  the  whole  divided  into 
parts,  the  general  divisions  being  so  called  by  way  of  eminence ;  the 
parts  are  subdivided  into  chapters;  these  into  sections;  these  into 
paragraphs ;  these  into  sentences ;  this  external,  formal  partition  cor- 
responding to  the  internal  logical  division  of  the  subject-matter.  So 
it  is,  in  matters  small  and  great,  we  are  governed,  though  for  the  most 
part  unconsciously,  by  logical  law ;  and  whoever  adjusts  his  notions  of 
things  according  to  their  true  relations,  in  systematic  order,  each  clear 
of  others  and  distinct  in  itself,  his  is  the  cultivated,  well-stored  intel- 
lect, he  is  eminently  the  thinker. 

§  8.  The  inaccuracy  in  the  usus  loquendi  of  familiar  words  requires 
that  they  should  be  largely  set  aside  in  building  up  a  science.  Hence 
nearly  every  science  has  many  unusual,  technical  terms,  sharply  de- 
fined, and  located  in  its  system :  such  words  as  are  not  likely  to  be 
drawn  into  vulgar  use,  and  have  their  edges  worn  off  by  the  attrition 
of  every-day  handling.  In  these  technicalities  a  science  arranges  its 
classifications  in  obedience  to  the  logical  principles  we  have  discussed, 
and  when  its  system  is  complete,  it  then  has  attained  that  logical  per- 


COMPLETE    SYSTEM.  73 

fection  which  is  specially  characteristic  of  science  according'  to  its 
ideal  definition. 

Owing  to  the  multiplied  divisions  in  sciences,  many  have  adopted- 
peculiar  names  also  for  the  several  subaltern  genera,  in  order  to  mark 
the  relative  place  of  each  step  in  the  ascending  and  descending  series 
of  classes,  and  thus  mark  out  clearly  and  conveniently  the  various  de- 
grees of  generalization.  Thus  the  system  of  Zoology,  as  given  by 
Agassiz,  slightly  modified  from  Cuvier,  is  as  follows : 


Second  Intentions. 


Kingdom, 
Branch. . . 
Class. . . 


Order. 


Family . 
Genus . . 
Species. 
Variety. 


First  Intentions. 


Animal,  Vegetable,  Mineral. 
Vertebrates,  Articulates,  Mollusks,  Radiates. 
Mammals,  Birds,  Reptiles,  Fishes,  etc. 
Bimana,  Quadrumana,  Carnivora,  Ilerbivora,  etc. 
Cats,  Dogs,  Civets,  Weasels,  Bears,  Seals,  etc. 
Felis  (the  true  Cat),  Lynxes,  etc. 
Lions,  Tigers,  Panthers,  Leopards,  etc. 
Nubian,  Arabian,  Persian,  Indian  Lions. 


The  student  of  Logic  would  do  well  to  make  a  thoughtful  visit  to 
any  well-arranged  Museum  of  Natural  History.  It  presents  a  logical 
universe.  The  summum  genus  is  material  product  of  nature.  On  en- 
tering he  finds  this  universe  logically  divided,  on  the  principle  of  suc- 
cession in  time,  perhaps  into  two  floors ;  the  lower  presenting  ancient 
products,  Geology ;  the  upper,  recent  products,  subdivided  into  Zoology 
and  Botany — extant  life,  in  opposition  to  the  extinct  life  in  the  lower 
division.  Between  these  two  floors  is,  perhaps,  a  gallery,  a  sort  of 
tertium  quid,  devoted  to  Lithology  and  Mineralogy.  We  enter  the 
lower  apartment,  the  Hall  of  Geology.  It  is  subdivided  into  two 
halls,  one  for  Paleontology,  the  other  for  Structural  Geology.  The 
first  of  these  has  many  co-ordinate  subdivisions,  the  ftmdamentum  di- 
visionis  being  again  historical.  At  first  glance  the  ground  seems  to  be 
size^  large  specimens  being  grouped  centrally  on  the  open  floor,  the 
small  being  in  side  cases.  But  these  large  specimens  mostly  belong 
to  the  same  geologic  age,  and  hence  the  fault  is  not  serious.  What- 
ever logical  offence,  however,  is  involved,  it  must  be  pardoned  as  prac- 
tically unavoidable.  The  side  cases,  we  observe,  are  labelled,  each  rep- 
resenting a  geologic  age ;  one  is  the  Silurian  age ;  another,  the  Devo- 
nian ;  another,  the  Carboniferous ;  and  so  on  in  the  order  of  time.  If 
we  approach  the  last  named,  we  find  it  subdivided  into  fossiliferous 
fauna  and  flora.  On  the  side  of  the  flora  we  find  one  set  of  shelves 
devoted  to  the  tribe  of  Phosnogams ;  another,  to  that  of  Calamites ; 


74  OF    CONCEPTS. 

another,  to  that  of  Cryptogams.  Looking  on  the  shelves  of  the  latter, 
we  find  the  Lepidodendrons,  the  Ferns,  and  the  Equisetse.  In  some 
cases  a  single  shelf  is  subdivided,  giving  infima  species,  and  then  at 
last  we  come  to  the  individual  specimens.  And  so  with  each  of  the 
other  departments.  In  this  distribution,  it  will  be  observed  that  the 
principle  of  succession  in  time  is  abandoned  when  we  come  to  the  in- 
terior of  the  case,  and  a  new  ground  of  division  adopted.  This  is  a 
logical  fault,  and  gives  rise  to  cross  divisions.  It  is,  however,  justified 
by  the  practical  results. 

If  these  collected  objects  were  arranged  merely  to  please  the  eye, 
they  might  furnish  amusement,  but  not  scientific  instruction.  It  is 
this  logical  arrangement  according  to  important  natural  affinities, 
evolving  a  complete  system,  that  distinguishes  this  museum  by  the 
specific  difference,  scientific.  As  a  product  of  thought,  it  offers  this 
peculiar  advantage  to  the  student  of  Logic,  that  it  presents  a  logical 
system  displayed,  not  in  words,  but  in  the  things  themselves. 

§  9.  We  now  close  this  general  division  of  Logic.  In  it  we  have 
considered  how  thought  does  and  must  elaborate  its  highest  and  most 
complete  results.  We  are  about  to  enter  upon  the  second  part,  which, 
however,  is  only  another  aspect  of  the  details.  Before  proceed- 
ing to  the  new  view,  attention  is  recalled  to  the  three  fundamental 
laws  which  govern  pure  thought  in  every  aspect.  Their  application 
at  each  step  has  been  so  obvious,  that  we  have  felt  it  needless  to  point 
it  out.  A  general  example  may  be  here  given.  If  any  genus,  X,  is  di- 
vided by  dichotomy  into  its  species,  A  and  non-A,  then  the  genus  X 
must  be  affirmed  of  both  these  species  in  turn  by  the  Law  of  Identi- 
ty ;  e.  g.,  Every  A  is  X,  and  Every  non-A  is  X.  The  species  must  be 
denied  of  each  other  by  the  Law  of  Contradiction  ;  e.  g.,  No  A  is  non-A. 
One  species  being  denied  of  a  thing,  the  other  must  be  affirmed  by 
the  Law  of  Excluded  Middle,  there  being  no  middle  ground ;  e.  g., 
Whatever  is  not  non-A  is  A.  Such  applications  should  be  constant- 
ly made  in  the  progress  of  the  subject.  The  Laws  should  never  be 
forgotten,  as  they  are  the  very  corner-stone,  the  root  of  the  whole 
Theory  of  Thought. 


PAKT  THIRD.— OF  JUDGMENTS. 


I.  THE   PROPOSITION. 

§  1.  To  judge  is  to  bring  one  thing  in  or  under  another.  A  judg* 
raent,  as  a  product  of  thought,  is  the  issue  or  result  of  comparison. 
Two  things  or  notions  compared  are  apprehended  as  similar  or  as  dis- 
similar, and  the  judgment  pronounces  that  they  agree  or  that  they  dis- 
agree. By  virtue  of  this  declared  relation,  the  duality  of  the  notions  is 
reduced  to  a  unity ;  the  two  terms  being  thought  in  relation  are  uni- 
fied. Necessarily  one  is  thought  as  determining  the  other.  For  both 
cannot  be  thought  as  merely  determining,  since  there  is  then  nothing 
determined.  On  the  other  hand,  both  cannot  be  thought  as  merely 
determined,  since  there  is  then  nothing  determining.  Hence,  one  must 
be  determining,  the  other  determined,  the  one  of  the  other.  Therefore, 
one  is  thought  as  an  attribute  or  mark  contained  in  the  other,  which  is 
thereby  determined ;  or  else  it  is  thought  as  a  class  which  the  other  is 
contained  under,  and  thereby  determined. 

Before  proceeding,  it  will  be  well  to  reiterate  that  the  considera- 
tions upon  which  we  are  entering  are  not  an  advance  beyond  those 
just  concluded.  We  are  not  to  advance,  since  the  arrangement  of 
thoughts  into  a  complete  system  is  logical  perfection.  We  are  to 
pass  again  over  a  portion  of  the  same  ground,  but  to  consider  it  from 
a  different  point  of  view.  The  almost  complete  identity  of  concept  and 
judgment  has  already  been  remarked.  A  concept  is  an  implicit  judg- 
ment ;  a  judgment  is  an  explicit  concept.  E.  g.,  "  Man"  is  a  concept 
that  implicitly  involves  the  marks  "  rational "  and  "  animal ;"  the  judg- 
ment "  Man  is  rational  and  animal "  differs  from  the  concept  only  in 
that  it  unfolds,  or  explicitly  states,  its  content.  We  are  not,  then, 
upon  new  ground.  It  is  sufficiently  apparent  that  in  forming  a  hie- 
rarchy of  concepts,  every  time  we  subordinate  or  co-ordinate  notions, 
at  every  step  of  division  or  definition,  we  pronounce  a  judgment. 
What  is  now  proposed  is  to  consider  the  parts  and  kinds  of  these 


76  OF    JUDGMENTS. 

judgments,  and  the  limiting  laws  which  regulate  their  formation  or 
determine  their  validity,  to  investigate  the  grounds  upon  which  we  do 
and  must  judge  in  determining  the  relations  of  our  concepts.  This  is 
true  not  only  of  immediate  judgment,  but  also  of  reasoning;  for  often- 
times we  cannot  determine  directly  the  relation  between  two  con- 
cepts, but  must  do  it  by  comparing  each  with  a  third.  Let  us, 
then,  keep  in  mind  that  in  what  follows  wre  are  only  improving  our 
knowledge  of  the  modes  by  which  the  mind  progresses  towards  com- 
pletely systematizing  its  thoughts.  And  let  us  also  remember  that 
every  step  is  governed  by  the  three  primary  laws,  and,  in  pure  Logic, 
by  no  others. 

§  2.  A  judgment  expressed  in  language  is  called  a  proposition. 
What  is  subjectively  a  judgment  is  objectively  a  proposition.  The 
first  treatment  is  to  sever  it  by  partition  into  three  portions.  These 
are,  according  to  what  was  said  above:  1st.  The  notion  of  some- 
thing determined,  called  the  Subject;  2d.  The  notion  of  some- 
thing determining,  called  the  Predicate ;  3d.  That  which  expresses 
this  recognized  relation  between  the  two,  called  the  Copula.  These 
terms  are  correlatives,  each  implies  the  existence  of,  neither  can  exist 
without,  the  other.  In  every  express  judgment  something  is  spoken  of 
— that  is  the  Subject ;  something  is  said  of  it — that  is  the  Predicate ; 
that  which  says  this— that  is  the  Copula.  Thus,  "  Snow  is  Pure ;" 
"Sin  is  Pardoned;"  "Sighs  are  Prayers;"  "some  Sentences  are 
Propositions;"  "some  Stars  are  Planets;"  or,  to  indicate  merely  the 
form,  "  S  is  P."  The  subject  and  predicate,  being  the  extreme  parts 
in  this  partition,  are  called  the  Terms  of  the  proposition.  It  is  not 
at  all  requisite  that  these  terms  should  consist  of  single  words ;  they 
may  be  composed  of  many  words  in  intricate  grammatical  relations. 
E.  g.,  "  The  very  many  difficulties  we  encounter  in  the  study  of  an  ab- 
struse science  (—subject)  are  (—copula)  to  be  overcome  by  persistent 
effort  stimulated  by  a  desire  to  acquire  knowledge"  (^predicate). 

"  With  taper  light 

To  seek  the  beauteous  eye  of  heaven  to  garnish  (—-subject) 
Is  (=copula)  wasteful  and  ridiculous  excess"  (^predicate). — ShaJcs. 

The  metaphysical  meaning  of  subject  and  substance  is  supposed  to 
be  understood.1  We  observe  that  the  logical  subject  must  always  be 
a  substantive  noun  (which  may  consist  of  many  words),  i.  e.,  some- 

1  See  Hamilton's  Metaphysics,  pp.  104  and  110. 


THE    PROPOSITION.  77 

thing  thought  of  as  having  substance.  Non-entis  nulla  sunt  predicata. 
The  predicate  may  be  either  substantive  or  adjective,  i.  e.,  attributive. 
We  may,  however,  take  the  view  that,  in  accordance  with  its  etymol- 
ogy, the  subject  means  that  which  is  thrown  under  or  contained  un- 
der the  predicate. 

§  3.  In  Aristotle  the  predicate  includes  the  copula,  and  this  is  still 
the  usage  of  grammarians.  But  logicians  now  reckon  the  copula  as  a 
distinct  co-ordinate  part.  Since  a  judgment  always  expresses  the 
present  relation  of  two  notions  now  in  mind,  the  copula  must  always 
appear  as  the  present  tense  of  the  verb  to  be.  E.  g.,  "  For  the  mind  is 
its  own  kingdom  in  which  an  eternal  now  does  always  last." 

The  copula  admits  of  only  one  qualification,  negation.  Hence  in 
a  negative  sentence  the  negative  particle,  wherever  it  may  occur,  is 
considered  as  a  part  of  the  copula.  E.  g.,  "  The  quality  of  mercy  is 
not  strained;"  "No  chastisement  is  joyous;"  "Britannia  needs  no 
bulwark,"  i.  e.,  Britannia  is  not  needing  a  bulwark. 

The  old  logicians  held  that  the  copula  may  be  otherwise  modified 
in  order  to  express  the  degree  of  certainty  that  attends  the  judgment. 
This  is  the  "  Doctrine  of  Modality."  Thus,— 

(  Problematic  ;  as,  A  may  be  B. 


Modal  judgments  are      ?™^\  as>  A  can  be  B- 

Impossible  ;  as,  A  cannot  be  B. 

v  Necessary  ;  as,  A  must  be  B. 

The  latter  two  are  called  "  Apodeictic"  or  "Demonstrative."  Recent 
logicians  reject  the  doctrine  of  modality,  and  account  the  modifiers  as 
a  part  of  the  predicate  ;  thus,  "  A  is  something  that  may  be  B." 
They  hold,  as  above  stated,  that  the  copula  can  be  modified  in  no  way 
whatever  except  by  the  negative  particle.8 

The  meaning  of  the  copula  is  ambiguous,  or,  rather,  it  has  quite  a 
number  of  different  significations.  In  a  following  section  it  will  be 
seen  that  it  may  be  interpreted  either  as  "  comprehends,"  or  as  "  is  con- 
tained under."  Thereafter  we  shall  find  that  it  sometimes  means  "  is 
equal  to  ;"  and  other  meanings  will  appear  as  we  progress.  We  need 
to  remark  here  only  that  it  requires  interpretation.  Always,  however, 
it  implies  existence,  modified  or  limited  by  the  predicate.  Aristotle 
says  :3  "  The  copula  affirms  merely  a  relative,  not  an  absolute,  exist- 

2  See  Hamilton's  Loyic,  p.  181  sq.  *  DC  Sophist-lei  Elenchi,  v,  3. 


78  OF    JUDGMENTS. 

ence."  From  "Ptolemy  is  dead,"  we  cannot  infer  that  "  Ptolemy  is" 
i.  e.,  actually  exists ;  but  only  that  he  exists  to  ns  as  a  dead  man  can, 
by  remembrance  or  tradition.  So,  "  Ptolemy  is  not  alive  "  denies  his 
existence  relative  to  life,  but  implies  it  in  the  other  sense. 

In  merely  existential  propositions  the  verb  to  be  declares  absolute 
existence,  it  is  both  copula  and  predicate.  Thus,  " I  am,"  " sum* 
means  "  I  am  existing,"  or  "  I  am  a  being."  The  predicate  in  such 
case  is  the  summum  genus,  or  its  single,  simple  mark.  So,  "  Enoch 
was  not ;"  "It  is  fine  weather  to-day;"  "There  was  a  sound  of  rev- 
elry by  night"  (Byron);  "There  is  none  that  doeth  good,  no  not 
one;"  "There  are  men  that  practise  self-denial,"  i.  e.,  some  exist, 
a  very  few.  Some  propositions  may  be  construed  as  existential  or 
otherwise ;  as,  "  It  is  impossible  to  love  and  be  wise  "  may  be  con- 
strued either  "To  love  and  be  wise  cannot  be"  i.  e.,  cannot  coexist, 
or  "  To  love  and  be  wise  is  impossible."  So,  "  There  are  six  Rich- 
monds  in  the  field."  So  also, — 

"  That  I  have  ta'en  away  this  old  man's  daughter, 
It  is  most  true ;  true,  I  have  married  her." — Shaks. 

That  is,  these  facts  exist ;  or,  these  accusations  are  true. 

Very  often  in  common  speech  the  copula  is  absorbed  in  verb  forms 
or  elided,  and  the  whole  proposition  may  consist  of  a  single  word. 
E.  g.,  "  Stars  twinkle,"  =  Stars  are  things  that  twinkle  ;  "  Cogito,"=I 
am  thinking;  "Pluit"=It  is  raining  (existential) ;  "  Ilium  fuit"  =^ 
Troy  is  something  which  formerly  existed  (existential);  "Did  he 
come  yesterday?"  Ans. — "Yes,"=He  is  one  who  came  yesterday; 
"He  loved,"  =  He  is  one  who  was  loving,  or  did  love.  All  verbs 
are  perhaps  fundamentally  one,  the  verb  "  to  be"  their  variety  aris- 
ing from  the  incorporation  of  various  attributive  notions  with  this 
simple  verbal  element,  and  its  own  past  and  future  forms  being  ad- 
verbial notions  incorporated  with  the  present  tense. 

§  4.  In  accordance  with  its  postulate,4  Logic  requires  that  all  propo- 
sitions shall  be  transformed,  as  in  the  above  examples,  so  that,  without 
addition,  retrenchment,  or  distortion  of  the  thought,  the  three  parts, 
Subject,  Copula,  Predicate,  shall  severally  appear.  The  process  is 
sometimes  quite  troublesome  and  awkward,  but  nevertheless  must  be 
performed.  E.  g.,  "So  he  said"  becomes  "What  has  just  been  said 

«  See  Part  1st,  ii,  §  8. 


THE    PROPOSITION.  79 

is  the  thing  which  he  said;"  "If  he  should  come  to-morrow,  he  will 
probably  stay  till  Monday  "  becomes  "  The  happening  of  his  arrival 
to-morrow  is  an  event  from  which  it  may  be  inferred  as  probable  that 
he  will  stay  till  Monday." 

It  may  be  observed  in  this  connection  that  the  proposition  often 
exhibits  rhetorical  inversions,  and  a  displacement  of  minor  parts. 
E.  g.,  "  Great  is  Diana  of  the  Ephesians ;"  "  Few  and  short  were 
the  prayers  we  said ;"  "  Flashed  all  their  sabres  bare  "  (Tennyson) ; 
"  Gold  and  silver  have  I  none,  but  such  as  I  have  give  I  to  thee ;" 

"  From  peak  to  peak  the  rattling  crags  among 
Leaps  the  live  thunder." — Byron. 

"  These  things  to  hear 
Would  Desdemona  seriously  incline." — Shaks. 

"  There  is  a  tide  in  the  affairs  of  men 
Which,  taken  at  the  flood,  leads  on  to  fortune." — Sliaks. 

As  the  subject  naturally  comes  first,  Logic  further  requires  that  order 
be  restored,  the  order  of  the  parts  as  stated  above.  All  such  inver- 
sions corrected,  all  elisions  supplied,  and  the  three  parts  stated  dis- 
tinctly in  their  natural  order,  constitute  the  reduction  of  a  proposition 
to  its  strict  logical  form.  Hence  every  proposition  must,  for  logical 
purposes,  be  reduced  to  one  or  the  other  of  the  two  invariable  forms : 
S  is  P,  or,  S  is  not  P. 

§  5.  Aristotle,  having  before  him  a  notion  or  thing,  asked  himself, 
what  and  how  many  kinds  of  things  may  be  predicated  of  it  ?  The 
result  was  his  ten  Categories  of  first  intentions.5  He  next  asked, 
what  and  how  many  are  the  kinds  of  predicates  ;  or,  in  other  words, 
what  are  the  second  intentions  of  all  possible  predicable  things  ?  The 
result  of  this  inquiry  was  his  equally  famous  doctrine  of  the  four 
Predicables.  It  is  that  every  judgment  affirms  or  denies  of  its  sub- 
ject one  or  the  other  of  these  four  relatives, — 

1st.  Definition ;  as,  Man  is  a  rational  animal  =  All  of  the  essence     )  Convertible 

2d.  Property ;  as,  Man  is  risible =None  of  the  essence  ) 

3d.  Genus ;  as,  Man  is  an  animal. =Part  of  the  essence  )  inconvert}ijie 

4th.  Accident ;  as,  Man  is  a  biped =Xone  of  the  essence  ) 

Aristotle  affirmed  that  every  judgment  is  in  the  form  of  one  or  another 
6  See  Fart  2d,  vii,  §  3. 


80  OP    JUDGMENTS. 

of  these  four  Predicables,  and  is  contained  under  one  or  another  of 
the  ten  Categories.  Porphyry  and  the  Schoolmen  enlarged  the  num- 
ber of  the  Predicables  to  five,  by  substituting  Species  (as  predicable 
of  individuals)  and  Specific  Difference  for  Definition.  This  was  the 
reverse  of  improvement;  for,  as  Aristotle  himself  had  remarked, 
each  of  these  is  of  the  nature  of  Genus,  and  interchangeable  with  it.' 
The  doctrine  of  the  Predicables,  however,  like  that  of  the  Categories, 
has  ceased  to  play  a  prominent  part  in  Logic.7 

§  6.  Various  divisions  are  made  of  judgments  or  propositions  for 
logical  purposes.  As  the  genus  divided  is  the  same  in  each  case,  and 
as  a  different  principle  is  used  in  each,  it  is  evident  that  there  will  be 
cross  divisions.  Thus,  an  intensive  judgment  may  be  either  affirm- 
ative or  negative ;  and  an  affirmative  judgment  may  be  either  inten- 
sive or  extensive.  This  is  not,  however,  a  logical  fault  here,  since  the 
several  divisions  are  not  proposed  as  steps  in  a  series,  but  are  inde- 
pendent of  each  other. 

The  first  division  to  be  considered  is  that  judgments  are  intensive 
and  extensive.  This  distinction  is  grounded  on  the  relation  of  sub- 
ject and  predicate,  as  containing  and  contained,  as  reciprocally  whole 
and  part.  In  the  intensive  judgment  the  subject  is  the  whole,  or 
major  term  ;  the  predicate  is  the  part,  or  minor  term.  Thus,  "  The 
earth  is  spherical."  Here  let  us  view  the  notion  "  earth  "  as  an.  inten- 
sive whole,  consisting  of  a  complement  of  marks.  We  then  attribute 
to  it  the  mark  "  spherical,"  which  thereby  enters  into,  or  is  recognized 
as  a  part  of,  this  whole ;  for  it  is  only  one  mark  out  of  many  that 
characterize  our  notion  "  earth."  This  is  an  attributive  judgment. 
It  is  conventionally  expressed  thus :  "  The  earth  comprehends  spheri- 
cal." On  the  other  hand,  in  the  extensive  judgment  the  predicate  is 
the  whole,  or  major  term ;  the  subject  is  the  part,  or  minor  term. 
Thus,  "  The  earth  is  a  sphere."  Here  let  us  view  the  notion  "  sphere  " 

8  Part  2d,  v,  §  3. 

7  See  Hansel's  Aldrich,  Appendix,  Note  A,  for  a  discussion  of  the  Predicables. 
The  doctrine  will  be  found  in  Topica,  i,  8,  where  Aristotle  says :  Every  predicate 
cither  reciprocates  with  its  subject,  or  does  not.  If  it  reciprocates,  it  expresses 
either  the  whole  essence  (TO  ri  yv  ilvai)  of  the  subject,  or  none;  in  the  former  case 
it  is  called  Definition ;  in  the  latter,  Property.  If  it  does  not,  it  expresses  either  a 
part  of  the  essence,  or  none.  In  the  former  case  it  must  be  a  part  of  the  defini- 
tion, either  Genus  or  Difference.  In  the  latter  case  it  is  evidently  Accident,  for 
accident  is  that  which  is  neither  definition  nor  property  nor  genus,  and  yet  is 
present  with  a  thing. 


THE    PROPOSITION.  81 

as  an  extensive  whole,  constituted  of  a  great  many  things,  such  as  the 
other  planets,  their  satellites,  the  sun,  all  globular  fruits,  the  geomet- 
rical sphere,  rain-drops,  etc.,  all  which  things  are  included 'under 
our  notion  "  sphere."  Now  in  the  given  judgment  we  declare  that 
the  earth  is  one  of  these  things,  a  part  of  the  great  complement  of 
things  denoted  by  "sphere."  It  is  conventionally  expressed  thus: 
"  The  earth  is  contained  under  sphere."  This  means :  "  My  notion 
of  the  earth  is  contained  under  my  notion  of  sphere."  For  another 
example :  "  Men  are  mortal ;"  this  is  intensive,  attributing  the  mark 
mortality  to  men,  the  major  term.  Again,  "  Men  are  mortals ;"  this 
is  extensive,  "  mortals "  is  the  major  term,  a  genus  embracing  also 
"brutes"  and  "plants,"  and  "men"  is  a  species  contained  under  this 
genus  which  is  predicated  of  it.  Let  it  be  remarked  how  the 
copula  is  here  interpreted  and  replaced  by  "comprehends"  and 
"  is  contained  under."  8 

Not  only  is  the  copula  ambiguous,  but  most  frequently  there  is 
nothing  in  the  entire  proposition  to  show  which  of  the  two  quantities 
is  thought.  And,  indeed,  mind  readily  passes  from  one  view  to  the 
other,  and  any  proposition  whatever  is  easily  capable  of  being  inter- 
preted cither  intensively  or  extensively.  While  this  is  of  logical  mo- 
ment, important  in  a  theory  of  thought,  it  is  not  of  the  smallest  prac- 
tical consequence.  One  person  might  peruse  a  volume  viewing  every 
proposition  intensively,  another  read  the  same  volume  viewing  every 
proposition  extensively,  and  the  knowledge  acquired  by  each  would 
not,  for  that  reason,  differ  appreciably.  It  is  a  fault  of  the  old  Logic, 
however,  that  all  of  its  nomenclature  and  treatment  has  exclusive 
reference  to  the  quantity  of  extension. 

This  seems  the  proper  place  to  observe  that,  while  a  logical  proposi- 
tion may  have  an  individual  subject,  it  cannot  have  an  individual 
predicate.  For  the  predicate  of  a  logical  proposition  in  extension  is 
a  genus ;  in  intension,  is  a  mark.  An  individual  can  neither  be  the 
one  nor  the  other.  We  may  say  "  Great  is  Diana ;"  but  this  is  a 
mere  rhetorical  inversion;  "Diana"  is  the  subject,  and  the  predicate 
is  "  great."  Again,  we  may  say  "  The  favorite  pupil  of  Plato  was 
Aristotle ;"  but  this  is  not  a  logical,  but  an  equivalent  proposition ; 
one,  not  in  the  qualitative,  but  in  the  quantitative  whole. 


8  Says  Arnauld :  "  J'appelle  comprehension  de  1'idee,  les  attributs  qu'elle  enferme 
en  soi.  J'appelle  etcndue  de  Tidee,  les  sujets  a  qui  cette  idee  convient." — Port' 
Royal  Logic,  pt.  i,  ch.  vi. 

6 


Sentences  are  •< 


82  OF    JUDGMENTS. 

§  7.  The  second  division  of  propositions  is  into  categorical  and  con- 
ditional. The  grammatical  forms  of  sentences  or  clauses,  since  they 
are  expressions  of  mental  states,  correspond  with  the  generic  faculties 
of  mind,  thus, — 

Interrogative,  \ 

Conditional,      >•  expressing  Cognition. 

Categorical,      ) 

Exclamatory,  "          Feeling. 

Optative,  "          Desire. 

I  Imperative,  "          Will. 

An  interrogative  sentence,  if  the  question  is  real  and  not  merely 
rhetorical,  shows  that  a  comparison  is  being  made  which  has  not  yet 
reached  an  issue  in  judgment.  It  is  the  search  after  ground  for  judg- 
ment. Conditional  sentences  or  propositions  express  a  comparison 
so  nearly  complete  that  only  certain  grounds  or  premises  remain  in 
question.  Such  doubtful  or  contingent  matter  is  stated  as  a  condi- 
tion. They  are  of  two  sorts,  conjunctive  and  disjunctive.  E.  g.,  "If 
you  understand  this,  you  can  explain  it ;"  and,  "  This  view  is  either 
accurate  or  inaccurate."  Conditional  propositions  arc  indicative,  sub- 
junctive, or  potential.  A  categorical  proposition  expresses  a  compari- 
son completed;  not  making  reference  to  any  condition,  it  is  absolute. 
It  also  appears  in  the  indicative,  subjunctive,  and  potential  moods. 
Logic  is  concerned  only  with  the  conditional  and  categorical  forms ; 
for  these  only  are  propositions,  none  of  the  other  four  forms  express- 
ing a  declaration.  The  consideration  of-  the  conditional  judgment  is 
postponed  until  we  shall  have  finished  our  examination  of  the  cate- 
gorical judgment.  For  the  present,  then,  the  words  judgment,  prop- 
osition, etc.,  unqualified,  will  be  understood  to  mean  the  categorical. 

The  term  "  categorical "  is  originally  legal,  it  means  "  accusing." 
In  Logic  it  means  a  downright  statement,  a  predication  or  attribution 
unqualified  by  condition,  and  hence  simple  or  absolute.  A  categori- 
cal proposition,  then,  is  one  in  which  the  predicate  is  unconditionally 
affirmed  or  denied  of  the  subject.8 

§  8.  The  third  division  of  judgments  is  into  total  and  partial.     It 

9  As  used  originally  by  Aristotle,  the  term  "  categorical "  meant  merely  "  affirma- 
tive," as  opposed  to  "  negative."  By  Theophrastus,  his  successor  in  the  Lyceum, 
it  was  employed  in  the  sense  "  absolute,"  "  simple,"  "  direct,"  as  opposed  to  "  con- 
ditional." In  this  signification  it  has  continued  to  be  employed  by  all  subsequent 
logicians.  See  Hamilton's  Logic,  p.  207. 


THE    PROPOSITION.  83 

is  called  their  Quantity.10  The  quantity  of  a  judgment  or  proposition 
is  determined  solely  by  the  quantity  of  the  subject,  according  as  this 
is  total  or  partial.  The  following  scheme  exhibits  the  important  di- 
visions,— 

f  Total  or  definite j  Individual,  e.  g.,  All  the  world's  a  stage. 

Propositions  are  -j  <  Universal,  e.  g.,  All  men  are  players. 

(  Partial  or  particular  j  Indefinite,  e.  g.,  Some  men  love. 

(  Semi-definite,  e.  g.,  Some  men  seek  reputation. 

The  quantity  of  the  subject,  and  hence  of  the  proposition,  is  indi- 
cated by  the  predesignations  all,  some,  etc.  It  is  often  the  case  that 
no  sign  of  quantity  is  prefixed.  A  judgment  always  has  quantity 
either  total  or  partial  in  the  mind  of  the  thinker  and  speaker,  but  the 
hearer  is  frequently  left  to  surmise  the  quantity  intended  from  the 
context,  or  from  the  matter.  Thus,  "  Birds  breathe,"  i.  e.,  all  do,  the 
predicate  being  of  the  essence ;  "  Birds  sing,"  i.  e.,  some  do,  the  mat- 
ter being  accidental  or  contingent.  Some  logicians  class  these  as  "  in- 
definite propositions,"  very  like  as  some  grammarians  specify  a"  doubt- 
ful gender."  But,  as  seen  in  the  scheme,  we  have  another  and  a  better 
use  for  the  word  "  indefinite,"  and  these  undetermined,  or,  as  Hamil- 
ton calls  them,  "  preindesignate  "  propositions,  do  not  properly  con- 
stitute a  class.  When  we  undertake  to  reduce  such  a  proposition  to 
strict  logical  form,  it  is  needful,  generally,  to  designate  the  quantity 
of  the  subject  by  its  sign. 

Individual  propositions  are  those  in  which  a  whole,  the  subject,  is 
judged  of  or  viewed  as  a  single,  indivisible  unity.  It  may  be  a  proper 
noun,  as,  "  Caesar  is  ambitious ;"  or  an  object  designated  as  an  indi- 
vidual by  the  definite  article,  or  by  any  demonstrative  word  or  phrase ; 
as,  "  The  world  is  round ;"  "  This  man  is  crazy ;"  "  The  whole  head 
is  sick,  and  the  whole  heart  faint ;"  "  All  Jerusalem  went  out  to  meet 
him."  It  may  be  a  collective  whole,  as,  "  The  senate  has  adjourned ;" 
"  The  college  of  Apostles  was  typified  in  the  twelve  tribes." 

Universal  propositions  have  subjects  which  are  logical  wholes.  The 
total  number  of  objects  within  a  divisible  but  undivided  class  are 
judged  of  ;  as,  "  All  men  are  players,"  i.  e.,  all  taken  together ;  "  Every 


10  This  term  is  unfortunately  ambiguous,  being  used  to  express  two  quite  differ- 
ent relations ;  the  quantity  of  thought  or  of  concepts  being  intensive  and  extensive, 
the  quantity  of  judgments  being  total  and  partial.  If  not  heeded,  this  various  ap- 
plication of  the  term  is  liable  to  confuse.  The  quantity  of  a  judgment  has  no  ref- 
erence whatever  to  intension  or  extension. 


84  OF    JUDGMENTS. 

man  is  a  player,"  i.  c.,  all  taken  severally.  Such  terms  are  said  to  be 
distributed ;  because  what  is  said  is  said  distributively  of  each  object 
in  the  class.  It  seems,  then,  that  "  All "  is  ambiguous,  meaning  either 
all  as  a  unity,  as  in  individual  propositions ;  or  all  as  a  plurality,  as  in 
universal  propositions.  The  former  is  called  the  cumular  meaning ;  the 
latter  is  called  the  exemplar,  and  is  its  most  usual  meaning.  The 
signs  of  universality  or  distribution  are  all,  every,  each,  both,  any,  none, 
neither,  always,  never,  whoever,  wherever,  etc.  Names  of  material  sub- 
stances, as  gold,  stone,  salt,  water,  flame,  etc.,  are  singular  and  universal 
without  predesignation.  They  each  denote  any  and  every  portion  of 
one  kind  of  substance. 

Partial  or  particular  propositions  are  those  in  which  we  judge  of  a 
number  of  objects,  less  than  the  whole  denoted  by  the  naked  subject. 
That  is,  we  judge  not  of  all,  but  only  of  some.  The  old  logical  mean- 
ing of  some  is  some  at  least,  perhaps  all ;  hence  it  is  only  "  may  be 
particular."  This  is  the  indefinite  some.  De  Morgan  proposes  to 
call  it  "  vague  "  instead  of  "  particular  "  or  "  indefinite ;  "  and  instead 
of  "  universal,"  he  proposes  "  full."  The  word  some  also  is  ambigu- 
ous ;  either  it  is  some  at  least,  perhaps  all,  as,  "  Some  men  love,"  per- 
haps all  do ;  or  it  is  some  at  most,  not  all,  as,  "  Some  men  seek  reputa- 
tion," not  all, — which  is  clearly  true  if  we  mean  only  that  reputation 
which  is  found  "  in  the  cannon's  mouth."  The  first  is  the  wholly  in- 
definite judgment;  the  second  is  the  semi-definite,  it  excludes  " all." 
Whether  the  predesignation  some  is  indefinite  or  semi-definite,  is  gen- 
erally to  be  determined  by  the  context  or  matter,  but  Hamilton,  who 
introduced  into  our  Logic  this  distinction,  which  he  considers  of  im- 
portance in  reasoning,  insists  that  some  is  always  thought  as  semi-def- 
inite when  the  other  term  of  the  judgment  is  universal ;  a  rule  that 
is  certainly  objectionable.11  A  subject  qualified  by  the  article  a  or  an 
(except  when  it  means  any)  is  particular  and  semi-definite  ;  as,  "  A  Ger- 
man invented  printing,"  i.  e.,  some  one  German  did.  If  we  substitute 
for  "  a  German  "  the  name  "  Faust,"  the  proposition  becomes  total  and 
individual.  The  signs  of  partial  or  particular  subjects  are  some,  not 
all,  not  every,  a  few,  there  are — that,  a  or  an,  one,  two,  three,  etc.,  some- 
times, somewhere,  etc.  There  are  also  signs  that  approximate  a  whole, 
but,  being  less  than  the  whole,  are  still,  if  taken  strictly,  partic- 
ular, though  in  common  speech  often  tantamount  to  all ;  as,  many, 
most,  almost  every  one,  the  large  majority  of,  etc.  The  following 

11  Sec  Appendix  to  his  Logic,  p.  531. 


THE    PROPOSITION.  85 

are  nearly  total  negatives  :  few,  very  few,  hardly  or  scarcely  any,  little, 
small,  slight,  rare,  seldom,  etc. ;  e.  g.,  "  Few  are  saved,"  i.  e.,  Nearly  all 
are  not,  perhaps  none ;  hence  indefinite.  But  a  few  is  affirmative ;"" 
e.g.,  "A  few  are  saved,"  i.  e.,  a  small  number  are,  perhaps  all;  hence 
indefinite.  Terms  qualified  by  such  signs,  or  merely  thought  as  par- 
ticular, are  said  to  be  undistributed. 

§  9.  The  fourth  division  of  judgments  is  into  positive  and  negative. 
The  positive  proposition  affirms,  by  the  Law  of  Identity,  that  the  sub- 
ject and  predicate  are  in  the  relation  of  equivalence,  or  in  that  of  part 
and  whole,  contained  and  containing.  The  negative  proposition  de- 
nies, by  the  Law  of  Contradiction,  such  relation,  excluding  subject  and 
predicate,  each  from  the  sphere  or  comprehension  of  the  other.  By 
the  principle  of  Excluded  Middle,  no  third  form  of  declaration  is  pos- 
sible; the  relation  in  question  between  subject  and  predicate  either 
does  or  does  not  exist,  it  is  yea  or  nay.  Hence,  as  has  been  said, 
every  proposition  is  of  the  form  "  S  is  P,"  or  "  S  is  not  P."  The 
ground  of  this  division  of  judgments  is  called  their  Quality.12 

But  let  us  examine  the  meaning  of  negation  a  little  more  particu- 
larly. Oftentimes  a  negative  judgment  simply  denies  one  thing  of 
another,  no  more.  If  we  say,  "  Smoke  is  not  vapor,"  the  meaning 
probably  is  that  these  two  notions,  though  liable  to  be  confounded, 
are  essentially  so  unlike  that  they  should  be  set  entirely  apart  in 
thought.  There  is  no  thought  of  a  genus.  It  is  simply  a  holding 
back  from  error.  So  also,  if  it  is  said,  "Smoke  is  not  fluid,"  the 
mark  is  simply  denied  as  comprehended  in  the  subject,  no  more. 
Again,  in  other  negative  judgments  there  is  a  thought  of  a  genus, 
which  is  denied  to  the  subject;  as,  "Smoke  is  not  a  gas;"  i.  e.,  the 
genus  gas  does  not  contain  under  it  smoke  as  one  of  its  kinds.  Smoke 
is  excluded  from  it,  simply  rejected  from  the  sphere  of  gases,  but  no 
more.  Or,  thirdly,  there  may  be  a  mental  reference  of  both  notions  to 
a  containing  genus,  under  which  they,  as  co-ordinate  species,  are  de- 
nied of  each  other ;  as,  "  Men  are  not  brutes."  Here  the  thought  is, 
most  likely,  limited  to  the  universe  animal,  while  man  and  brute,  as 
co-exclusive  and  exhaustive  of  the  genus,  are  thought  as  contradic- 
tories. Lastly,  the  notions  may  be  thought  merely  as  disparate,  or 


13  Another  unfortunate  confusion  of  terms,  for  the  quality  of  judgments  as  pos- 
itive or  negative  has  no  reference  whatever  to  the  quality  of  concepts  heretofore 
discussed. 


86  OF   JUDGMENTS. 

perhaps  contrary,  and  as  such  denied  of  eacli  other ;  as,  "  Man  is  not 
a  beast  for  burdens,  nor  a  reptile  for  bruising ;"  or,  "  See  Folly  waltzing 
far  from  Wisdom's  way,"  i.  e.,  Folly's  way  is  not  Wisdom's  way.  In 
this  case,  also,  there  is  a  thought  of  a  containing  genus  or  universe 
limiting  the  notions,  which  .have  much  in  common,  to  a  narrow 
sphere. 

In  a  negative  judgment  the  negative  particle  qualifies  the  copula, 
though  it  may  not  stand  in  connection  with  it.  E.  g.,  "  Not  a  drum 
was  heard"  (Wolfe);  "Not  every  mistake  is  culpable;"  "No  man  is 
wiser  for  his  learning"  (Selden) ;  "No  drunkard  shall  inherit  eternal 
life ;"  "  There  is  none  that  doeth  good,  no,  not  one ;"  "  That  goodness 
is  no  name,  and  happiness  no  dream"  (Byron).  A  negative  judgment 
is  said  to  have  "  a  negative  copula,"  which  phrase,  taken  strictly,  is  a 
contradiction  in  terms,  but  is  used  to  designate  the  qualified  copula. 
'It  is  needful  to  observe  that  affirmative  propositions  often  contain 
negatives  as  a  part  either  of  the  subject  or  of  the  predicate,  and  should 
not  be  mistaken  for  negative  propositions.  E.  g.,  "  Not  to  know  me 
argues  yourself  unknown"  (Milton);  "lie  that  does  not  heed,  stum- 
bles ;"  "  To  wonder  not  is  a  rare  art,"  "  Nil  admirari  prope  res  cst 
una  "  (Horace).  In  those  the  negative  is  a  part  of  the  subject.  In  the 
following  it  is  in  the  predicate:  "Even  in  that  extremity  the  general 
cry  was,  No  surrender "  (Macaulay) ;  "  On  iny  bended  knees  I  sup- 
plicate you,  reject  not  this  bill  "  (Brougham) ;  "  We  cannot  do  without 
it."  It  should  also  be  remarked  that  propositions  arc  often  essential- 
ly negative,  wherein  no  negative  particle  appears.  E.  g.,  "  The  brute 
perishes ;"  "  He  is  blind ;"  "  Darkness  and  silence  fall  on  land  and 
sea."  These  also  are,  in  form,  logical  affirmatives.  Negative  thought 
may  also  be  conveyed  in  affirmative  forms  by  means  of  such  phrases 
as  beyond,  far  from,  the  reverse  of,  on  the  contrary,  wanting  or  deficient 
in,  devoid  of,  and  the  like. 

When  the  negative  particle  qualifies  the  predicate,  the  judgment 
is  affirmative;  it  is  not  a  mere  denial,  but  something  is  affirmed 
of  the  subject,  though  the  predicate  is  a  negative  notion.  We  have 
already  remarked  that  many  notions,  originally  pure  negatives,  have 
in  usage  had  thought  into  them  a  positive  character.13  These  are  no 
longer  pure,  and  are  generally  accompanied  by  the  thought  of  a  narrow 
genus  or  universe,  which. is  not  the  case  in  a  pure  negation ;  e.  g.,  help- 
Lss,  unpleasant,  unwell,  uneven,  indirect,  immortal,  etc.  Thus,  if  I 

13  See  supra,  Part  2d,  vi,  §  5. 


THE    PROPOSITION.  87 

say  "  The  soul  is  immortal,"  there  is  affirmed  of  it,  besides  the  neg- 
ative notion  of  infinity,  the  positive  notion  of  continuous  existence. 
This  is  a  thought  very  different  from  that  of  the  pure  negative  "  non- 
mortal."  But  it  is  impracticable  to  analyze  exhaustively  the  various 
shades  of  meaning  thus  acquired.  So,  setting  them  aside,  we  shall 
speak  only  of  purely  negative  predicates. 

Affirmative  judgments,  having  a  predicate  purely  negative,  combine 
an  act  of  affirmation  with  an  act  of  negation.  These  have  been  class- 
ed by  Kant  as  a  third  species  under  quality,  the  negativo-affirmative, 
called  by  him  "  Infinite  or  Limitative  Judgments."  It  will  be  best  to 
give  Kant's  own  explanation,  as  follows : 

44  In  transcendental  Logic,  infinite  must  be  distinguished  from  affir- 
mative judgments,  although  in  general  Logic  they  are  rightly  enough 
classed  under  affirmative.  General  Logic  abstracts  all  content  of  the 
predicate  (though  it  be  negative),  and  only  considers  whether  the  said 
predicate  be  affirmed  or  denied. of  the  subject.  But  transcendental 
Logic  considers  also  the  worth  or  content  of  this  logical  affirmation, 
an  affirmation  by  means  of  a  merely  negative  predicate,  and  inquires 
how  much  the  sum  total  of  our  cognition  gains  by  the  affirmation. 
For  example,  if  I- say  of  the  soul,  "It  is  not  mortal,"  by  this  nega- 
tive judgment  I  should  at  least  ward  off  error.  Now  by  the  proposi- 
tion "  The  soul  is  non-mortal,"  I  have,  in  respect  of  the  logical  form, 
really  affirmed,  inasmuch  as  I  thereby  place  the  soul  in  the  unlimited 
sphere  of  non-mortal  beings.  Now,  because,  of  the  whole  sphere  of 
possible  existences,  the  mortal  occupies  one  part,  and  the  non-mortal 
the  other,  neither  more  nor  less  is  affirmed  by  the  proposition  than 
that  the  soul  is  one  among  the  infinite  multitude  of  things  which  re- 
main over  when  I  take  away  the  whole  mortal  part.  But  by  this 
proceeding  we  accomplish  only  this  much,  that  the  infinite  sphere  of 
all  possible  existences  is  in  so  far  limited  that  the  mortal  is  excluded 
from  it,  and  the  soul  is  placed  in  the  remaining  part  of  the  extent  of 
this  sphere.  But  this  part  remains,  nothwithstanding  this  exception, 
infinite,  and  more  and  more  parts  may  be  taken  away  from  the  whole 
sphere  without  in  the  slightest  degree  thereby  augmenting  or  affirma- 
tively determining  our  conception  of  the  soul.  These  judgments, 
therefore,  infinite  in  respect  of  their  logical  extent,  are,  in  respect  of 
the  content  of  their  cognition,  merely  limitative." * 

It  remains  to  state  here  the  Aristotelic  rule  for  the  distribution  of 

14  Critique  of  Pure  Reason,  p.  59.— Meiklejolm's  Tr. 


88  „  OF   JUDGMENTS, 

the  predicate.  We  have  shown  in  the  previous  section  that  the  dis- 
tribution of  the  subject  is  according  to  the  quantity  of  the  judgment ; 
that  universals  distribute,  and  particulars  do  not  distribute,  the  subject. 
Now  the  distribution  of  the  predicate,  which  takes  place  in  thought 
without  any  verbal  sign,  depends  on  the  quality  of  the  judgment. 
The  RULE  is:  Negatives  distribute  the  predicate,  affirmatives  do  not. 
Some  simple  examples  will  suffice  to  illustrate  this  rule.  Thus, 
"All  houses  are  buildings,"  i.e.,  some  buildings  only,  for  there  are 
some  buildings  that  are  not  houses,  as  forts,  bridges,  ships,  etc. ; 
hence  this  predicate  is  undistributed  or  particular.  Again,  "  No  houses 
are  pyramids ;"  i.  e.,  not  any  pyramids,  since  no  pyramid  can  be  called 
a  house ;  hence  this  predicate  is  distributed  or  universal.  Again, 
"  Some  houses  are  dwellings,"  i.  e.,  some  dwellings  only,  for  tents, 
caves,  and  ships  also  are  dwellings ;  hence  the  predicate  is  particular. 
Again,  "  Some  houses  are  not  dwellings,"  i.  e.,  some  houses,  such  as 
shops,  factories,  churches,  are  not  any  dwellings ;  hence  the  predicate 
is  here  universal. 

It  is  evident  that  this  rule,  which  comes  from  the  old  Logic,  and 
which  Hamilton,  as  we  shall  see,  impugns  as  altogether  defective,  has 
exclusive  reference  to  the  extension  of  the  terms.  Its  view  is  that 
when  we  affirm,  we  thereby  include  the  subject  in  the  class  denoted 
by  the  predicate  as  merely  a  part  of  it ;  and  that  when  we  deny,  we 
thereby  exclude  the  subject  from  that  class  wholly. 

§  10.  In  order  to  facilitate  the  statement  and  analysis  of  the  syllo- 
gism, logicians  combine  the  quantity  and  quality  of  judgments.  There 
result  four  forms,  which  they  symbolize  by  vowel  letters,15  as  exhibited 
in  the  following 

TABLE  OF  THE  PROPOSITIONAL  FORMS. 

Quantity.       Quality.     Symbols.  Formulae.  Examples. 

Universal  Affirmative, — A — All  S  is  (some)  P All  oaks  are  (some)  trees. 

Universal  Negative,     — E — No  S  is  (any)  P No  oaks  are  (any)  vines. 

Particular  Affirmative, —  I — Some  S  is  (some)  P Some  are  (some)  evergreens. 

Particular  Negative,    — 0 — Some  S  is  not  (any)  P.  ..Some  are  not  (any)  shrubs. 

"  It  is  curious  to  note  that  these  symbolic  letters  were  first  adopted  by  an  old 
logician,  Petrus  HSspanus;  they  being  the  first  two  vowels  in  the  words  affiwao  and 
nego.  We  may  add  that  the  old  logicians  abounded  in  mnemonic  devices,  and,  ac- 
cordingly, the  said  Petrus  supplied  the  following  stanza, — 

Asserit  A,  negat  E,  sed  universaliter  ambae ; 
Asserit  I,  negat  0,  sed  particulariter  ambo. 


THE    PROPOSITION. 

Individual  propositions  (§  8),  since  the  subject  is  a  total,  arc  usual- 
ly considered  as  universal,  and  symbolized  by  A  and  E. 

§  11.  The  fifth  division  is  of  propositions  rather  than  of  judgments. 
Propositions  are  Simple,  Complex,  and  Compound. 

A  Simple  proposition  consists  of  only  one  judgment;  i.  e.,  it  con- 
tains not  more  than  one  subject  and  one  predicate.  It  may,  however, 
consist  of  many  grammatical  elements ;  as,  "  Well-organized  and  skil- 
fully administered  governments  are  productive  of  happiness  in  their 
subjects." 

A  Complex  proposition  involves  with  the  principal  judgment  one 
or  more  subordinate  or  incidental  judgments.  This  subordinate  ele- 
ment appears  as  a  clause,  incidental  to  the  principal  subject  or  predi- 
cate. E.  g.,  "  A  man  who  is  learned  is  respected  ;"  "  Whoever  is  right 
is  safe ;"  "  Who  steals  my  purse,  steals  trash  "  (Shaks.) ;  "  A  little 
fire  is  quickly  trodden  out,  which,  being  suffered,  rivers  cannot  quench" 
(Shaks.);  "Ill  blows  the  wind  that  profits  nobody"  (Shaks.).  In 
these  the  clause  is  in  the  subject,  though  the  latter  two  are,  the  first 
partly,  the  second  wholly,  inverted.  In  the  following  the  clause  is  in 
the  predicate :  "  I  am  monarch  of  all  /  survey  "  (Cowper) ;  "  The 
cry  is  still  *  They  come."1 "  (Shaks.) ;  "  When  I  ivas  a  boy,  I  used  al- 
ways to  choose  the  wrong  side"  (Johnson);  "  When  the  age  is  in, 
the  wit  is  out "  (Shaks.) ;  "  What  I  have  written,  I  have  written." 
In  the  following  there  are  incidental  clauses  in  both  subject  and  pred- 
icate :  "  They  that  are  ivise  shall  shine  as  the  stars  (shine) ;"  "  Shylock, 
who  was  a  hard-hearted  man,  exacted  the  payment  of  the  money  he 
lent  with  such  severity  that  he  ivas  much  disliked  by  all  good  men" 
(Lamb). 

A  subdivision  of  incidental  clauses  may  be  made  into  Explicative 
and  Limitative,  or  Restrictive.  The  Explicative  clause  merely  unfolds 
the  marks  connoted  by  the  notion  it  qualifies;  as,  "Man,  who  is  born 
of  woman,  is  of  few  days  and  full  of  trouble;"  "Jonah  sought  to 
evade  the  God  who  is  omnipresent"  Explicative  clauses  express  judg- 
ments not  now  made,  but  formerly  made,  and  now  renewed  subordi- 
nately.  Limitative  or  restrictive  clauses,  which  may  also  be  allowed 
to  include  the  concessive  clause  removing  restriction,  are  those  which, 
as  the  terms  indicate,  limit  or  restrict  the  notion  they  qualify ;  as, 
"  Men  who  are  avaricious  are  discontented."  This  is  not  said  of  all 
men,  but  is  said  of  all  in  a  limited  class.  So,  "  He  is  well  paid  that 
is  well  satisfied"  (Shaks.) ;  "  Honesty,  when  it  is  mere  policy,  is  not  a 


90  OF   JUDGMENTS. 

virtue."  The  concession  in  "  I  will  trust  him  though  he  slay  me  "  re- 
moves a  conceivable  restriction.  So  in  "  Live  we  how  we  can,  yet  die 
we  must "  (Shaks.).  In  "  They  strive  that  they  may  enter  in"  and 
"  They  take  heed  lest  they  fall"  the  predicates  are  limited  by  purpose ; 
one  positively,  the  other  negatively.  When  the  restrictive  is  a  condi- 
tion, the  categorical  proposition  may  easily  be  converted  into  a  con- 
ditional. Thus  the  example  above  may  become  "  If  men  are  avari- 
cious, they  are  discontented." 

We  now  observe  that,  these  incidental  clauses  of  all  kinds  being  re- 
garded merely  as  substantive,  adjective,  or  adverbial  elements,  the 
complex  proposition  is  in  Logic  treated  as  simple.  It  was  needful  to 
discuss  it  only  that  we  may  be  forewarned  not  to  mistake  clauses  for 
principal  propositions ;  and,  in  reducing  a  proposition  to  strict  logical 
form,  that  we  may  be  careful  to  subordinate  them  in  place  to  the  prin- 
cipal subject  or  predicate.  Thus,  "  He,  who,  though  he  is  rich,  is  sav- 
ing, is  one  that  can  share  with  him  ivho  is  needy  without  lessening 
what  is  enjoyed  ;"  here  the  form  is,  S  is  P.  Indeed,  the  complex  sen- 
tence is  often  directly  reducible  to  one  that  is  strictly  simple.  Thus, 
the  first  example  given  above,  "  A  man  who  is  learned  is  respected," 
reduces  to  "  A  man  of  learning,"  or  "  A  learned  man,  is  respected." 

The  Compound  proposition  is  one  that  comprises  two  or  more 
judgments,  co-ordinate,  or  nearly  so ;  and  these,  for  logical  purposes, 
require  to  be  separated  and  stated  independently.  It  is  of  two  kinds, 
according  as  the  compounding  elements  are  more  or  less  obvious. 
The  first  kind,  wherein  these  elements  are  quite  evident,  has  received 
no  specific  name,  and  needs  only  the  illustration  of  a  few  examples ; 
as,  "Art  is  long,  and  life  is  fleeting"  (Longfellow) ;  "Every  man  de- 
sireth  to  live  long,  but  no  man  would  be  old  "  (Swift). 

"  We  are  such  stuff 

As  dreams  are  made  on ;  and  our  little  life 
Is  rounded  with  a  sleep." — Shaks. 

"  Men  may  come,  and  men  may  go, 
But  I  go  on  forever." — Tennyson's  Brook. 

"  Veni,  vidi,  vici"  contains  three  distinct  propositions  in  three  words. 
"Pompey,  Crassus,  and  Caesar  were  triumvirs;"  here  are  three  prop- 
ositions: 1st.  "  Pompey  was  a  triumvir;'*  2d.  "Crassus  was  a  trium- 
vir ;"  3d.  "  Caesar  was  a  triumvir."  If,  however,  we  say  "  Pompey, 
Crassus,  and  Cassar  were  the  triumvirs,"  then  the  proposition  is  single 
and  simple,  for  the  three  are  taken  collectively  as  one  whole.  So, 
"Koses  and  lilies  contend  for  a  home  in  her  cheek,"  is  single  and 


THE    PROPOSITION.  91 

simple;  but  in  "Darkness  and  silence  settle  on  land  and  on  sea," 
there  are  four  propositions. 

"  Ho  !  hearts,  tongues,  figures,  scribes,  bards,  poets  cannot 
Think,  speak,  cast,  write,  sing,  number, — hoo  ! — 
His  love  to  Antony." — Shaks. 

In  this  curious  sentence  there  are  six  distinct  propositions,  and  were 
it  not  that  each  predicate  answers  to  its  own  subject  we  might  count 
thirty-six. 

Compound  propositions  of  the  second  class,  having  elements  less 
obvious,  and  requiring  analysis,  are  for  this  reason  called  Exponibles. 
These  more  than  the  others  require  special  attention,  since  they  are 
more  intricate,  and  in  syllogizing  with  them  it  is  often  requisite  that 
they  be  distinctly  resolved.  We  name  three  species:  1st.  Exclusives 
and  Exceptives ;  2d.  Comparatives ;  and  3d.  Inceptives  and  De'sitives. 

1st.  EXCLUSIVES.     Compounds  of  this  species  may  be  formulated 

thus : 

AisB. ..  ..=A 


=  (Nonon-AisB ..=E 

E.  g,  "Faith  alone  justifies"=  \  ™th  Josti^  . 

(  What  is  not  faith  does  not  justify. 

It  is  obvious  that  this  proposition  may  be  inverted  and  the  exclusive 
particle  made  to  appear  in  the  predicate;  thus,  "Justification  is  by 
faith  alone,"  =  15  is  only  A. 

Exceptives  are  exemplified  in  "  All  but  one  were  saved,"  which 
means  "  Nearly  all  were  saved  "  and  "  One  was  not  saved ;"  I  and  O. 

No  useful  rule  can  be  given  for  the  resolution  of  these  two  forms 
of  exponibles.  Generally,  if  not  always,  the  elementary  judgments 
differ  in  quality,  and  one  is  to  be  noted  as  direct  and  the  other  as  in- 
direct or  implied.  The  distinction  between  the  exclusive  and  excep- 
tive forms  is  of  no  practical  moment,  as  they  are  readily  convertible, 
the  only  difference  being  that  what  is  the  direct  judgment  in  the  one 
becomes  the  indirect  in  the  other.  The  following  are  some  of  the  ex- 
clusive and  exceptive  particles :  only,  alonet  exclusively,  merely,  sole, 
solely,  but,  etc.  These  particles  annexed  to  the  subject  quantify  the 
predicate  universally ;  as,  *'  God  alone  is  wise,"  i.  e.,  He  is  all  the  wise. 
Annexed  to  the  predicate  they  merely  limit  the  subject  to  that  predi- 
cate ;  as,  "  The  sacraments  are  but  two,"  i.  e.,  there  are  no  more. 

"Wo  give  some  examples  illustrating  their  various-  modes  of  ex- 
pression to  facilitate  the  recognition  of  them  hereafter.  "  None  but 
the  brave  deserve  the  fair "  (Dryden) ;  "  A  fool  thinks  none  except 


92  OF    JUDGMENTS. 

himself  wise  ;"  "  Brutus,  in  killing  Caesar,  was  merely  patriotic ;" 
"  Christ  is  the  only  Saviour ;"  "  The  moon  is  only  our  satellite ;"  or, 
"  is  our  only  satellite ;"  "  Mercy  but  murders,  pardoning  those  that 
kill"  (Shaks.);  "The  paths  of  glory  lead  but  to  the  grave"  (Gray); 
"God  alone  is  worthy  of  being  loved  for  his  own  sake,"  i.  e.,  we 
ought  to  love  God  for  his  own  sake,  and  all  other  things  for  God's 
sake ;  "  Only  those  riches  which  you  shall  have  given  away  will  al- 
ways abide  with  you,"  "  Quas  dederis  solas  sender  habebis  opes  "  (Mar- 
tial, Ep.  v,  43).  Sometimes  the  exclusive  or  exceptive  particle  is  in 
the  sense,  but  not  expressed ;  as,  "  (There  is  only)  one  Lord,  one  faith, 
one  baptism  "  (Eph.  iv,  5). 

2d.  COMPARATIVES.  Propositions  in  which  we  compare  contain 
two  judgments;  for  it  is  one  to  say  that  a  thing  is  such,  and  one 
other  to  say  that  it  is  more  or  less  so  than  another  thing.  Thus, 
the  maxim  of  Epicurus,  that  "  Pain  is  the  greatest  of  evils,"  affirms 
that  pain  is  an  evil,  and  that  it  is  the  extreme  one.  This  is  more 
evident  when  we  consider  that  the  maxim  may  be  contradicted  in 
two  ways.  The  Stoics  denied  the  first  component,  saying  that  no 
pain  is  an  evil.  The  Peripatetics,  however,  allowed  the  first  compo- 
nent, but  denied  the  second,  saying  that  vice  is  the  extreme  evil. 
But  why  may  not  the  same  be  said  of  any  proposition  having  a  quali- 
fied predicate,  as  "  Pain  is  a  great  evil  ?"  Because  what  is  said  here 
merely  excludes  other  evils ;  but  in  the  above  comparative  other  evils 
are  expressly  included  by  what  is  said. 

3d.  INCEPTIVES  and  DESITIVES.  When  we  say  that  a  thing  has 
commenced,  or  ceased  to  be,  such,  we  make  two  statements,  one  about 
the  thing  as  before,  the  other  as  after,  the  time  indicated.  Thus, 
"I  begin  to  believe"  affirms  that  I  now  believe,  and  that  heretofore 
I  did  not  believe ;  and  "  I  have  ceased  to  believe"  affirms  the  two  con- 
traries. Observe  that  to  say  simply  "I  believe"  says  nothing  of  the 
past.  Again,  "With  Augustus  Home  began  to  be  marble,"  and, 
"  With  Augustus  Ptome  ceased  to  be  of  brick."  These  may  fairly  be 
interpreted  as  saying,  "Augustus  found  Rome  of  brick,  and  left  it 
marble."  That  inceptivcs  and  desitives  are  compounds  becomes  a  little 
more  evident  when  we  consider  that  a  question  such  as  "Have  you 
quit  drinking  2"  affirms  the  component  that  you  have  been  drinking, 
and  questions  only  the  second,  whether  you  are  now  drinking. 

It  should  be  observed  that  many  judgments  which  are  not  classed 
as  compound,  whose  outward  form  is  simply  "  S  is  P,"  nevertheless 
imply  in  thought  an  indirect  judgment.  This  is  true  of  every  semi- 


THE    PROPOSITION.  93 

definite  judgment  (§  8).  Sometimes,  on  the  other  hand,  we  convey 
our  thoughts  by  indirections  expressed ;  we  merely  "  insinuate,"  leav- 
ing the  direct  judgment,  our  real  meaning,  to  be  understood.  Logic 
always  deals  primarily  with  the  latter,  and,  according  to  its  postulate, 
gives  it  complete  expression.1" 

§  12.  A  sixth  division  is  of  judgments  rather  than  of  propositions. 
It  is  exhibited  in  the  following  scheme : 

Analytic a  priori. 

Judgments  are 


Synthetic  \  a  Postcriori  or  empirical. 
(  a  priori  or  pure. 


a  priori  or  pure. 

When  the  predicate  P  belongs  to  the  subject  S  as  something  which 
is  contained,  though  covertly,  in  the  concept  S,  the  judgment  is  called 
Analytic.  Since  the  predicate  adds  nothing  to  the  conception  of  the 
subject,  but  only  unfolds  its  constituent  marks,  which  are  thought 
already,  though  confusedly,  in  the  subject,  it  is  also  called  Explicative. 
E.  g.,  All  bodies  are  extended.  I  need  not  go  beyond  the  concept 
body  in  order  to  iind  extension  connected  with  it,  but  need  merely 
to  analyze  the  conception  in  order  to  discover  this  predicate  in  it. 
The  analytic  judgment  is  a  priori.  It  is  not  grounded  on  experience, 
because  I  need  not  go  out  of  the  sphere  of  my  conceptions  to  form  it, 
and  hence  resort  to  the  testimony  of  experience  is  quite  unnecessary. 
That  bodies  are  extended  is  not  an  empirical  judgment,  but  itself 
stands  firm  a  priori.  It  is  a  necessary  judgment,  its  necessity  arising 
from  the  ground  of  identity.  Analytic  judgments  are  highly  impor- 
tant, but  are  so  only  because  by  them  we  attain  the  distinctness  of 
conception  which  is  requisite  for  a  sure  and  extended  synthesis  in  the 
progress  of  knowledge. 

When,  however,  the  predicate  P  lies  completely  out  of  the  concept. 
S,  though  connected  with  it,  the  judgment  is  called  Synthetic.  Since 
the  predicate  increases  the  conception  of  the  subject  by  something 
which  was  not  contained  in  it,  which  no  analysis  could  have  discov- 
ered in  it,  this  judgment  is  also  called  Augmentative  or  Ampliative. 
E.  g.,  All  bodies  are  heavy.  This  predicate  is  something  totally 


16  The  above  analysis  of  compound  propositions,  derived  mostly  from  Arnauld, 
is  intended  to  serve  logical  purposes,  and  is  not  even  for  these  supposed  to  be  ex- 
haustive. To  the  student  of  Logic  it  will  be  sufficient  in  most  cases,  and  generally 
illustrative  and  helpful. 


94  OF    JUDGMENTS. 

different  from  what  I  necessarily  think  as  contained  in  the  concept 
body,  and  adds  to  the  content  of  that  notion. 

Synthetic  judgments  are  subdivided  into  those  a  posteriori  and 
those  a  priori.  The  former  are  judgments  from  experience,  which  as 
such  are  always  synthetical.  I  cognize  by  analysis  the  concept  body 
through  the  marks  extension  and  impenetrability.  But  now  I  augment 
my  knowledge.  Looking  back  on  my  experience  of  body,  I  find 
weight  always  connected  with  the  above  marks ;  so  I  amplify  my  con- 
ception by  predicating  of  it  this  additional  mark,  saying,  Body  is  heavy. 
Experience  is  the  ground  of  this  synthesis,  because  the  notions  body 
and  weight,  though  one  is  not  contained  in  the  other,  still  belong  to 
one  another  contingently  as  parts  of  a  whole  of  experience. 

But  synthetic  judgments  a  priori  are  not  grounded  on  experience, 
nor  does  experience  help  us  at  all  in  forming  them.  E.  g.,  Every 
event  has  a  cause.  The  concept  event  implies  antecedent  time,  from 
which  I  could  form  an  analytic  judgment.  But  the  conception  of  a 
cause  lies  quite  out  of  the  concept  event,  and  indicates  a  thing  en- 
tirely different.  This  judgment,  therefore  is  not  analytic.  Moreover, 
the  experience  from  which  I  derive  the  conception  of  event  does  not 
include  an  experience  of  cause,  and  hence  experience  is  not  the  ground 
of  the  judgment.  Again,  the  judgment  has  a  universality  which  ex- 
perience can  never  give,  expressing  a  necessity  that  cannot  come  of 
experience,  which  is  essentially  contingent.  Such  a  judgment  is, 
therefore,  altogether  a  priori.  What,  then,  is  its  ground  ?  How  is  a 
synthetic  judgment  a  priori  possible?  This  is  the  question  which 
Kant  undertook  to  answer  in  his  Critique  of  Pure  Reason.  Its  im- 
portance is  inestimable,  for  upon  this  class  of  synthetic  or  ampliative 
judgments  depends  the  whole  of  speculative  knowledge.17 

§'  13.  Under  a  previous  topic18  we  considered  two  kinds  of  wholes 
in  or  under  which  mind  contemplates  its  objects — the  logical,  or  qual- 
itative, and  the  mathematical,  or  quantitative,  whole.  Under  the  pres- 
ent topic  we  have  thus  far  considered  judgment  as  in  the  former  only, 

17  See  Introduction  to  Kritik  der  reincn  Vernunft,  §  4.     The  distinction  of  prop- 
ositions into  Verbal  and  Real  made  by  Mill  (Logic,  bk.  i,  ch.  vi),  followed  by  Bain 
(Logic,  bk.  i,  ch.  ii,  §  7),  seems  substantially  the  same  as  the  above  famous  distinc- 
tion by  Kant  of  judgments  into  Analytic  and  Synthetic.     Those  logicians  reject, 
however,  the  class  of  synthetic  judgments  a  priori,  and  consider  all  synthetic  judg- 
ments or  real  propositions  to  be  a  posteriori  or  empirical. 

18  Part  2d,  vi,  §  2.     See  also  Hamilton's  Locjic,  pp.  379,  380. 


THE    PROPOSITION.  95 

and  now  something  must  be  said  of  it  when  in  the  latter  whole.19 
For  what  we  think  about  is  conceived  of  either  as  general  or  as  indi- 
vidual. We  attain  generality  only  by  virtue  of  the  qualities  of  things ; 
and  to  think  things  in  respect  of  their  qualities  is  to  think  them  in 
the  qualitative  or  logical  whole.  On  the  other  hand,  we  may  contem- 
plate the  object  of  thought  as  a  quantity,  possessing  no  generality, 
not  divisible  into  kinds,  individual,  severable  only  by  dissection  into 
adjacent  parts,  and  measurable  by  some  ideal  standard.  This  we  call 
thinking  in  the  quantitative  or  mathematical  whole. 

Things  of  the  same  kind  often  differ  in  degree;  and  since  in  judg- 
ments concerning  them  the  comparison  is  not  respecting  qualities  or 
kinds,  but  respecting  the  quantity  in  its  different  degrees,  we  will  vent- 
ure to  call  these  Judgments  of  Degree. 

Two  mathematical  quantities  can  be  related  to  each  other  in  two 
degrees  only ;  they  must  be  either  equal  to  each  other,  or  else  one 
greater  than  the  other,  either  indefinitely  or  by  so  much.  Hence  the 
copula  in  these  judgments  either  means  " is  equal  to"  " is  the  same 
as"  or  it  is  "  is  greater  than"  or,  in  the  reverse  view,  "  is  less  than" 
It  may  be  replaced  by  the  sign  of  equality  (=•),  or  of  inequality  (>) ; 
for  such  a  proposition  is  an  equation.  E.  g.,  "  The  earth's  diameter 
is  (=)  8000  miles;"  "The  earth  is  greater  than  (>)  the  moon." 

According  to  this  statement,  every  judgment  in  the  comparative 
degree,  or  judgment  of  comparison,  has  for  its  copula  "is  greater 
than"  or  its  converse  or  obverse,  "  is  less  than."  This  simple  rela- 
tion is  often  compounded  with  other  notions;  as  in  "longer"  and 
in  "shorter,"  in  "included  by,"  "better,"  "worse,"  "stronger," 
"  more  repulsive,"  "  most  attractive,"  "  highest,"  etc.  But,  in  brief, 
any  terms  whatever  expressive  of  degree  of  comparison  involve  this 
copula,  and  characterize  the  judgment  as  essentially  mathematical. 

Here  the  question  concerning  the  meaning  of  the  copula  recurs. 
We  have  seen  that  in  the  logical  proposition  it  is  to  be  interpreted 
"  comprehends"  or  "  is  contained  under;"  and  no  one  perhaps  will  ques- 
tion that  in  the  strictly  equivalent  proposition  it  means  " is  equal  to" 
or  "  is  the  same  as."  These  three  relations,  therefore,  are  ambiguous- 
ly conveyed  by  the  simple  "  is."  Now  a  judgment  or  proposition  is 


19  A  double  sense  of  the  word  "quantity"  has  already  been  pointed  out.  We 
are  now  obliged  to  use  it  in  still  a  third  sense,  one  that  has  no  reference  whatever 
to  intensive  and  extensive  thought,  nor  to  the  logical" distribution  of  terms,  but  in 
a  sense  more  strictly  mathematical,  as  relating  to  individual  totals. 


96  OF    JUDGMENTS. 

a  declared  relation  between  two  notions  or  terms.  Can  all  relations 
be  reduced  to  these  three?  Are  there  not  others?  De  Morgan  in- 
sists that  relations  essentially  distinct  are  very  numerous,  and  proposes 
to  include  them  all  in  one  generalized  " copula  of  relation,"  thus: 
"Every  X  has  a  relation  to  some  Y,"  embracing  the  above,  and  also 
such  connectives  as  in  "  X  controls  Y,"  "  X  causes  Y,"  and  many  oth- 
ers. We  shall  subsequently  see  there  is  no  need  for  this  great  ex- 
tension of  the  copuiar  meaning;  but  there  appears  to  be  a  necessity 
for  adding  "is  greater  than"  and  its  obverse  to  the  meaning  com- 
monly recognized  in  Logic.  It  is  true  that  a  comparative  judgment 
can  be  construed  as  compound.  Thus,  "  The  mass  of  the  earth  is  a 
mass  greater  than  that  of  the  moon"  means,  as  we  have  seen  in  the 
preceding  section,  "  The  mass  of  the  earth  is  as  much  as  the  mass 
of  the  moon,  and  has  something  in  addition."  But  if  the  comparison 
be  accepted  as  an  expressed  interpretation  of  the  copula,  then  com- 
parative propositions  would  seem  to  be  in  thought  quite  simple. 
When  I  mentally  compare  the  masses  of  two  planets,  I  judge  simply 
and  directly  that  one  is  greater  than  the  other,  without  at  all  thinking 
that  one  is  as  much  as  the  other,  and  has  something  to  spare.  The 
copula  thus  understood,  and  the  proposition  construed  as  mathemat- 
ical, many  difficulties  arising  from  syllogistic  law  disappear.29 

Both  terms  of  judgments  of  degree  are  always  individuals  viewed 
as  mathematical  wholes.  There  are  various  modes  of  designating  in- 
dividuals, such  as  by  the  definite  article,  by  demonstrative  and  possess- 
ive pronouns,  etc. ;  e.  g.,  "  Thou  art  the  man  ;"  "  This  is  our  home." 
These  are  integral  wholes.  Collective  wholes  often  occur ;  e.  g.,  "  A 
legion  is  ten  cohorts."  Another  mode  is  by  a  proper  name,  or  by 
some  particular  mark ;  as,  "  Aristotle  is  the  Father  of  Logic."  Every 
proposition  whose  predicate  is  quantified,  as  "all"  or  "some,"  is 

30  The  two  copulas  above  described  express  the  relation  of  degree  between  two 
individual  wholes.  The  relation  between  the  whole  and  its  parts,  merely  as  such, 
is  expressed  by  the  copula  "is  part  of;"  e.  g.,  "  The  thumb  is  part  o/the  hand  ;" 
"An  arc  is  a  part  o/the  circle."  This  is  a  quantitative  judgment  of  a  different 
kind  from  that  of  degree,  but  does  not  seem  to  require  especial  exposition. 

It  is  worthy  of  note  that  "comprehends"  in  the  qualitative  whole  is  similar 
to  "  is  greater  than'1'1  in  the  quantitative ;  and  "  is  contained  under"  is  strikingly  liko 
"  is  less  than."  But  there  is  another  correspondence  more  real.  AVe  quantitative- 
ly as  well  as  qualitatively  think  the  relation  of  whole  and  part,  and  "  is  contained 
under"  corresponds  to  "is  apart  of."  For  example, — 

The  preachers  are  contained  under  (or,  are  a  class  of)  teachers. 
The  preachers  are  a  part  of  (or,  arc  a  section  of)  the  teachers. 


THE    PROPOSITION.  97 

thereby  brought  into  the  mathematical  whole,  and  the  "  all"  is  not 
distributive,  but  cumular ;  e.  g.,  "  All  men  are  all  reasoncrs ;"  "  Ducks 
are  some  birds."  Here  both  terms  are  individual  totals.  The  alge- 
braic equation,  as,  "6  =  2x3,"  and  'V— /  =  (a;+y)  (ar—y),"  is  a 
judgment  of  the  same  character,  its  two  members  are  individuals. 
All  such  judgments  are  properly  called  quantitative,  because  primari- 
ly, fundamentally,  and  essentially  they  always  relate  to  space  or  time, 
the  bases  of  mathematics,  the  science  of  quantity. 

An  individual  may  be  known  by  the  test  that  its  parts  are  not  kinds. 
We  have  seen  in  §  6  that  an  individual  cannot  become  a  predicate  in 
the  logical  whole.  In  the  mathematical  whole  the  predicate,  as  well 
as  the  subject,  being  always  an  individual,  the  individual  predicate  is, 
therefore,  the  characteristic  mark  of  a  judgment  of  degree. 

A  consequent  peculiarity  of  these  propositions,  and  a  test  of  their 
equivalency,  is  that  they  are  all  simply  convertible.  No  special  sym- 
bol is  needed.  Since  the  subjects  are  total,  they  are  treated  like  indi- 
vidual propositions  (§  8),  and  symbolized  by  A  and  E  (§  10),  with  this 
marked  difference,  that  whereas  individual  propositions  are  inconver- 
tible (ii,  §  7),  the  proposition  of  degree  is  always  and  only  simply 
convertible.  When  the  terms  are  not  equivalent,  the  copula  "  is  great- 
er than"  must  in  conversion  be  substituted  by  " is  less  than"  and. 
vice  versa.  When  they  are  equivalent,  either  term  may  be  substituted 
wherever  the  other  occurs. 

Singular  terms  must  be  discriminated  from  individual,  with  which 
they  are  apt  to  be  confounded.  "A  man"  is  a  logical  qualitative 
whole,  meaning  "  one  single  member  of  the  class  man,"  and  is  a 
thought  very  different  from  "  That  man,"  which  is  a  mathematical, 
quantitative  whole.  The  first  is  singular;  the  second,  individual. 
Singular  propositions  are  liable  to  be  confused  with  equivalent  propo- 
sitions, because  of  the  oneness  of  the  terms  in  both ;  but  surely  it  is 
evident  enough  that  in  "  A  horse  is  an  animal "  there  is  generality 
and  no  equivalence ;  whereas  in  "  This  horse  is  my  animal "  there  is 
equivalence  and  no  generality. 

Likewise  let  us  distinguish  between  coextensive  and  equivalent  no- 
tions. Two  coextensive  logical  wholes  are  aptly  symbolized  by  two 
concentric  circles  whose  radii  arc  equal.  But  it  should  be  kept  in 
mind  that  these  circles  are  mathematical  quantities,  and  hence  are 
equivalent,  or  rather  equal.  But  coextcnsion  belongs  to  the  logical 
whole,  and  is  essentially  qualitative.  The  following  are  coextensive 
notions :  "  Honesty  and  probity  ;"  "  Triangle  and  trilateral ;"  "  En- 


98  OF    JUDGMENTS. 

dogens  and  monocotyledons ;"  "  Acotyledons  and  flowerless  plants ;" 
"Double-refracting  and  polarizing  crystals;"  "To  conquer  one's  pas- 
sions and  to  become  master  of  one's  self."  But  when  the  fact  of  co- 
extension  is  neither  expressed  nor  thought  of,  i.  e.,  whenever  the  judg- 
ment containing  such  terms  in  extension  is  simple,  the  subject  is  con- 
strued in  thought  as  contained  under  the  predicate.  And  when  the 
coextension  is  thought,  still  the  copula  cannot  be  replaced  by  the 
sign  of  equality  and  read  "  is  equal  to"  but  it  should  be  read  "  is  co- 
extensive with." 

Also  we  must  not  be  embarrassed  by  the  factitious  generality  of 
many  quantitative  propositions,  and  doubt  that  the  terms  are  individual 
totals.  "  A=B ;"  this  means,  "  The  quantity  A  is  equal  to  the  quan- 
tity B ;"  or,  since  equal  quantities,  purely  as  such,  are  indistinguish- 
able, "  The  quantity  of  A  is  the  same  as  (is  identical  with)  the  quan- 
tity of  B."  "  Men  are  stronger  than  boys  "  means  "  The  strength  of 
men  is  greater  than  the  strength  of  boys."  "Every  diameter  is  a 
double  radius  "  means  "  The  length  of  every  diameter  is  equal  to  the 
length  of  two  radii."  "  The  superior  planets  move  more  slowly  than 
the  inferior "  means  "  The  speed  of  the  superior  is  less  than  that  of 
the  inferior."  "  Iron  is  not  as  heavy  as  lead  "  means  "  The  specific 
gravity  of  iron  .is  less  than  that  of  lead."  "  Circus  jokes  arc  old  as 
the  hills  "  means  "  The  age  of  the  one  is  equal  to  that  of  the  other." 
"  Women  love  best "  means  "  Woman's  love  is  greater  than  any  other." 
"  The  color  of  her  eyes  is  the  color  of  the  skies."  It  will  be  noticed 
that  mere  abstract  qualities  are  thought  quantitatively,  i.  e.,  as  indi- 
vidual totals,  and  when  abstract,  if  indistinguishable  as  greater  and 
less,  are  identified  by  "  is  the  same  as." 

It  remains  to  observe  that  the  logical  and  the  mathematical  wholes 
are  often  readily  convertible  in  thought,  such  transference  requiring 
few  verbal  changes  or  none  to  adapt  the  expression  to  the  mode  of 
thought.  Thus  "  Mankind,"  which  in  the  very  form  of  the  word  ex- 
presses a  general  notion  containing  under  it  species,  may  be  replaced 
by  "  The  human  race,"  which  is  individual,  having  no  species,  and 
can  only  be  partitioned  into  sections.  So  there  are  kinds  of  army ;  and 
there  are  wings  of  an  army.  Being  or  thing  is  general,  including  all 
kinds  of  existing  things ;  but  the  Universe  is  not  a  general  notion, 
but  a  mathematical  whole,  a  collection  of  all  things  into  a  unit,  the 
only  one  not  a  part  of  any  other,  and  is  capable  only  of  dissection. 
Again,  the  term  animal  is  general ;  but  animals  may  be  thought  as 
a  collective  whole  comprising  many  individuals  similar  in  certain  (is- 


THE    PROPOSITION.  99 

sential  respects,  and  this  whole  may  be  severed  by  thought  into  parts, 
such  as  the  part  saved  in  the  ark,  and  the  part  destroyed  by  the 
deluge.  The  indefinite  article  qualifying  a  predicate  may  be  inter- 
preted in  either  of  two  ways ;  thus  "  Gold  is  a  metal "  means  logi- 
cally and  strictly  that  gold  is  a  kind  of  metal,  but  we  may  think  it 
mathematically,  that  gold  is  a  part  of  metals  taken  as  a  collective 
whole.  In  short,  perhaps  any  general  notion  may  be  thus  transmuted 
or  reduced  in  thought  to  a  mathematical  quantity,  a  collective  whole 
consisting  of  many  similar  individuals,  its  species  becoming  dissev- 
ered members. 

This  weighty  fact,  and  the  essential  difference  between  the  two  modes 
of  thought,  not  being  recognized,  is  the  reason,  I  apprehend,  why 
Hamilton  and  a  number  of  subsequent  logicians  have  attempted  the 
reduction  of  all  propositions  to  equations,  and  proposed  thereby  to 
supersede  the  old  logical  system.21  But  such  reduction  is  artificial. 
It  exhibits  the  processes  of  thinking,  not  as  they  really  occur,  but  in 
forms  into  which  they  may  be  construed  by  more  or  less  violence. 
Such  a  presentation  of  Logic  is  possible  only  because  of  the  power 
which  the  mind  has  of  transmuting  its  notions  from  logical  wholes 
and  parts  into  mathematical  wholes  and  parts. 

On  the  other  hand,  the  old  Logic  was  limited  to  the  logical  whole 
and  part.  A  Latin  logician  would  probably  deny  that  what  we  have 
called  a  judgment  of  degree  is  a  case  of  predication  at  all — predication 
belonging  only  to  the  logical  relation — and  would  insist  on  all  such 
forms  being  construed  in  the  logical  whole.  Hence,  perhaps,  no  sym- 
bol was  assigned  to  such  propositions,  nor  were  they  otherwise  recog- 
nized. But  these  propositions  abound,  they  are  in  constant  use,  they 
frequently  stand  as  premises  in  all  kinds  of  reasonings,  and  mathemat- 
ics consists  of  them.  We  may,  it  is  true,  transmute  them  into  prop- 
ositions strictly  logical,  but  we  then  incur  the  most  serious  embarrass- 
ments in  the  attempt  to  bring  them  under  syllogistic  law.  Moreover, 
this  again  is  artificial,  not  natural,  not  thought  as  it  is,  for  we  reason 
with  mathematical  propositions  without  any  such  transference.  It  is 
needful,  then,  to  admit  them  to  a  prominent  and  important  position 
in  Logic  if  we  would  truly  represent  human  thinking. 


3i  Notably  George  Boole  in  his  MatJiematical  Analysis  of  Logic  (1847),  and  his 
Investigation  of  the  Laws  of  Thought.  A  very  good  resume  of  his  principles  will 
be  found  in  Bain's  Logic,  pp.  1 90-207.  Jevons  would  make  Logic  mechanical ! 
See  his  "  Logical  Machine,"  facing  the  title  of  his  Principles  of  Science. 


100  OF    JUDGMENTS. 

§  14.  Praxis.  In  each  of  the  following  propositions,  is  the  form 
categorical,  or  conditional,  or  what?  (§  7).  If  categorical,  is  it  sim- 
ple, or  complex,  or  compound?  (§  11).  If  simple  or  complex,  re- 
duce to  strict  logical  form  (§  4),  and  interpret  the  copula  (§  6). 
Affix  the  symbol  of  quantity  and  quality  (§  10).  If  compound,  re- 
solve it  into  its  elements,  and  affix  the  symbol  to  each.  If  mathe- 
matical, express  it  as  an  equation  or  inequality. 

1.  It  is  the  duty  of  every  man  to  fear  God  and  honor  the  king. 

2.  Very  few  patriots  are  disinterested.    There  is  no  place  like  home. 
0.  Nothino-  is  harmless  that  is  mistaken  for  virtue. 

O 

4.  Men  are  all  sinners.     No  news  is  good  news. 

5.  All  these  claims  upon  my  time  overpower  me. 

6.  One  truth  is  clear,  whatever  is,  is  right. — Pope. 

7.  Not  many  if  any  metals  are  without  lustre. 

8.  Not  being  rich  is  not  always  an  evil.     Diogenes  was  no  fool. 

9.  Except  the  self -existent,  there  is  nothing  beautiful,  but  that  which 

is  not. — Rousseau. 

10.  Hardly  any  virtue  is  safe  from  passing  into  vice. 

11.  Virtue  is  teachable,  if  it  is  knowledge. 

12.  All  is  not  gold  that  glitters.     The  rich  are  not  therefore  happy. 

13.  None  but  Aryans  are  capable  of  the  highest  civilization. 

14.  Jefferson  was  the  father  of  the  University  of  Virginia. 

15.  Ah !  few  shall  part  where  many  meet, 

The  snow  shall  be  their  winding  sheet. —  Campbell. 
1C.  Charity  affords  relief  as  far  as  possible. 

17.  He  who  truly  loves  most  is  not  he  who  flatters. 

18.  The  quarrel  toucheth  none,  but  us  alone. — Shaks. 

19.  After  his  death,  resistance  and  order  were  no  more. — Gibbon. 

20.  I  propose  my  thoughts  only  as  conjectures. — Burnet. 

21.  Whereto  serves  mercy,  but  to  confront  the  visage  of  offence? 

22.  That  thou  art  happy,  owe  to  God. — Milton. 

23.  George  Eliot  is  Mrs.  Lewes.     Arrows  are  swifter  than  eagles. 

24.  Though  this  be  madness,  yet  there's  method  in  it. — Shaks. 

25.  Those  here  present  constitute  the  class  in  Logic. 

26.  There  is  no  fireside,  howsoe'er  defended, 
But  has  one  vacant  chair. — Longfellow. 

27.  Saltpetre  is  nitrate  of  potassa.     That  horse  won  the  race. 

28.  There  are  who  ask  not  if  thine  eye  be  on  them. —  Wordsworth. 

29.  There's  a  divinity  that  shapes  our  ends, 
Rough  hew  them  how  we  will. — Shaks. 


THE    PROPOSITION.  101 

30.  The  time  has  been  my  senses  would  have  cooled  to  hear  a  night 

shriek. — Shaks. 

31.  Nothing  is  so  easy  as  to  object.     He  is  as  wise  as  Solomon. 

32.  Some  books  are  to  be  tasted,  others  to  be  swallowed,  and  some 

few  to  be  chewed  and  digested. — Bacon,  Essay  L. 

33.  Our  revels  now  are  ended.     There's  few  or  none  do  know  me. 

34.  Who  lived  king,  but  I  could  dig  his  grave  ? — Shaks. 

35.  The  longer  the  day,  the  shorter  the  night. 

36.  That  he  is  mad,  'tis  true  ;  'tis  true,  'tis  pity ; 
And  pity  'tis  'tis  true. — Shaks. 

37.  There's  not  a  joy  the  world  can  give, 
Like  that  it  takes  away. — Byron. 

38.  His  alms  are  far  beyond  his  means. 

39.  I  will  not  let  thee  go,  unless  thou  bless  me. 

40.  The  author  of  Novum  Organum  was  not  the  inventor  of  Falstaff. 

41.  Even  a  fool,  when  he  holdeth  his  peace,  is  counted  wise. 

42.  It  will  hardly  be  sufficient  to  resolve  only  a  few  of  these  examples. 

43.  The  most  skilful  of  generals  was  Napoleon. 

44.  Every  sly  act  is  nothing  less  (or  else)  than  dishonest. 

45.  Logic  is  the  science  of  the  necessary  forms  of  thought. 

46.  Not  every  one  that  saith  unto  me,  Lord,  Lord,  shall  enter  in,  but 

he  that  doeth  the  will  of  my  Father. 

47.  A  circle  is  the  figure  of  greatest  area. 

48.  Your  duties  are  not  another's.     My  tasks  are  all  but  impossible. 

49.  He  was  too  impulsive  a  man  not  to  have  committed  many  errors. 

50.  Yonder  forest  is  the  refuge  of  outlaws. 

51.  He  first  and  last  will  reign  sole  king. — Milton. 

52.  Congress  legislates  for  the  Union. 

53.  Mankind  are  all  men  and  women.    All  testimony  is  merely  probable. 

54.  God's  word,  exclusively,  is  to  be  received  without  question. 

55.  The  most  sublime  act  is  to  put  another  before  thee. 

56.  Le  salut  des  vaincus  est  de  n'en  point  attcndrc. — Tr.from  Virgil. 

57.  Nobilitas  sola  est  atque  unica  virtus. — Juv.  Sat.  viii,  20. 

58.  Nullas  habet  spes  Troja,  si  tales  habet. — Seneca. 

59.  Nemo  Ia3ditur,  nisi  a  seipso. — Id. 

60.  Melior  est  sapientia  quam  vires,  et  vir  prudens  quam  fortes. 

61.  Latin  has  been  a  dead  language  for  five  hundred  years. 

62.  That  which  survives  is  the  fittest. 


102  OF    JUDGMENTS. 


II.  INFERENCES. 

§  1.  Under  the  previous  topic  we  have  examined  seven  modes  of 
dividing  judgments  or  propositions.  An  eighth  remains,  so  important 
that  each  part  calls  for  separate  and  extended  consideration.  This 
division  is  grounded  on  the  various  processes  by  which  judgments  are 
formed,  and  may  be  stated  as  follows : 

(  Intuitions. 
Judgments  are  <  (  Inductive. 

(  Inferences.  -J  (  Im mediate. 

(  Deductive,  -J 

(  Mediate. 

Intuitions  are  the  synthetic  judgments  of  Kant  already  described, 
one  kind  being  empirical,  the  other  pure.  These  are  the  ground  of 
all  knowledge,  the  ultimate  premises  from  which  arise  all  other  judg- 
ments. They  lie  on  the  threshold  of  Logic,  but  their  discussion  be- 
longs to  Philosophy,  the  science  of  principles. 

Inferences  are  defined  by  Aristotle  to  be  "  enunciations  in  which, 
from  something  laid  down  and  admitted,  something  distinct  from  what 
we  have  laid  down  follows  of  necessity."  Locke  says,  "  To  infer  is 
nothing  but,  by  virtue  of  one  proposition  laid  down  as  true,  to  draw  in 
(inferre)  another  as  true."  Says  Mill :  "  It  is  the  act  of  drawing  a 
conclusion  from  premises."  More  generally,  to  infer  is  to  derive  a 
judgment  from  one  or  more  premised  judgments. 

Inductive  inferences  are  synthetic.  They  are  universal  judgments 
derived  from  particular  cases  of  empirical  intuition,  and  furnishing 
premises  for  subsequent  deduction.  Their  importance  is  so  great 
that  an  adequate  discussion  of  them  will  require  a  distinct  treatise. 

Deductive  inferences  are  analytic.  They  are  inferred  judgments  of 
equal  or  less  generality  than  that  of  the  premises.  They  are  the  sub- 
ject of  Deductive  Logic,  and  are  of  two  kinds,  immediate  and  mediate. 

When  two  notions  known  as  related  are,  in  a  modified  form,  con- 
cluded of  each  other  without  the  intervention  of  a  third  notion  as  a 
medium  of  comparison,  the  inference  is  immediate.  In  this  case  one 
judgment  is  derived  directly  from  another.  There  is  but  one  premise, 
the  given  judgment ;  and  the  derived  judgment  merely  represents  the 
given  matter  in  a  modified  form. 


INFERENCES.  103 

A  mediate  inference  or  a  reasoning  is  accomplished  through  a  third 
notion  used  as  a  medium  of  comparison.  It  has  two  premises. 

Immediate  inference  will  be  treated  under  the  present  general  topic. 
Mediate  inference,  or  Reasoning,  is  the  subject  of  the  subsequent  part. 

§  2.  Let  us  at  the  outset,  for  the  sake  of  clearness,  distinguish  be- 
tween implied  and  inferred  judgments,  which  McCosh  would  identify.1 
An  implied  judgment  is  one  that  actually  exists  together  with  the 
given  judgment,  either  merely  in  thought  or  involved  covertly  in  the 
expression.  An  inferred  judgment  is  one  that  only  virtually  or  po- 
tentially exists  in  the  given  judgment,  and  is  derived  from  it.  The 
statement  of  the  one  is  nothing  new ;  there  is  no  advance,  no  progress 
of  thought,  but  only  its  full  expression ;  that  of  the  other  contains 
something  new,  there  is  a  step  forward,  a  progress  of  thought.  In 
the  inferred  judgment  there  is  always  either  a  different  subject,  or  a 
different  predicate,  from  that  of  the  premise,  and  perhaps  both. 

The  different  quantities  of  thought,  the  intensive  and  extensive,  are 
hardly,  in  strictness,  to  be  considered  as  implying  each  other,  much 
less  can  we  consider  that  one  is  inferred  from  the  other;  they  are 
merely  different  aspects  of  the  same  thing,  which  necessarily  coexist, 
one  having  merely  accidental  preponderance  in  thought. 

In  indirect  speech  there  is  always  an  implied  judgment.  So  also  the 
semi-definite  proposition  involves  an  implied  judgment.  Thus,  if  I  say 
"  Some  men  are  rich,"  it  is  accompanied  by  the  thought  that  "  Some 
men  are  not  rich;"  but  this,  being  an  actually  coexistent  thought, 
is  not  inferred.  It  would  be  evidently  an  entirely  unwarranted  use 
of  the  term  to  say  that  one  of  these  judgments  is  inferred  from  the 
other.  We  cannot  say  that  since  some  men  are  rich,  then  it  follows 
that  some  men  are  not  rich.  An  exponible  contains  an  implied,  in- 
direct judgment  which  is  expressed,  though  covertly.  Thus,  the  ex- 
ample given  might  be  stated,  "  Only  some  men  are  rich."  Here, 
"  Only  some  "  expresses  covertly  that  some  are  not. 

Again,  what  Thomson,  followed  by  McCosh,  calls  "Immediate  In- 
ferences of  Interpretation  "  are  not  inferences,  but  mere  implications. 
Thus,  in  "  John  loves  Mary,"  it  is  implied,  but  not  inferred,  that  "John 
lives,"  that  "  Mary  lives,"  and  that  "  There  is  such  a  thing  as  love." a 


1  Logic,  p.  108.     Cf.  Mill's  Logic,  bk.  ii,  cb.  i,.§  2  ;  and  Thomson's  Outline,  §  83. 
a  Thomson's  Outline,  §  89 ;  and  McCosh's  Logic,  p.  115.    Refer  also  to  what  was 
said  of  the  force  of  the  copula,  i,  §  3. 


104  OF    JUDGMENTS. 

Finally,  the  "  Immediate  Inference  by  the  Sum  of  several  Predi- 
cates "  of  Thomson  and  McCosb,  is  not  an  inference  at  all,  but  merely 
a  compound  judgment  of  the  obvious  sort.  Thus,  "  Copper  is  red, 
malleable,  ductile,  and  tenacious  "  is  merely  compounded  of  "  Copper 
is  red,"  "  Copper  is  malleable,"  etc.  It  is  strange  phrasing  to  call  it 
an  inference  from  these  components.  It  is  also  quite  remarkable 
that  McCosh  includes  under  this  head  the  bringing  together  the  com- 
ponents of  a  definition. 

§  3.  As  preparatory  to  an  account  of  those  several  kinds  of  im- 
mediate inference  for  which  we  shall  have  subsequent  use,  we  state  a 
prohibition  applicable  to  all  deductions  in  the  form  of  the  following 
RULE  :  The  quantification  must  not  be  increased.  We  may  infer  from 
all  to  all,  from  some  to  some,  from  all  to  some,  but  not  from  some  to 
all.  It  is  sufficiently  evident  that  what  is  said  only  of  some  furnishes 
no  ground  for  a  statement  concerning  all. 

§  4.  Active  and  Passive.  The  change  from  active  to  passive,  and 
vice  versa,  is  the  first  form  of  immediate  inference  to  be  noticed.  The 
two  forms  are  usually  regarded  as  merely  equipollent,  but  they  seem 
to  be  rather  an  inference,  the  one  from  the  other.  In  "  God  made  the 
world,"  something  is  said  of  "  God ;"  he  is  the  subject  of  thought. 
In  "  The  world  was  made  by  God,"  the  subject  is  u  The  world,"  and 
something  is  said  of  it.  The  inversion,  too,  is  only  partial,  since  the 
notion  "  made  "  is  in  the  predicate  in  both  cases.  Hence  I  would  pre- 
fer to  consider  this  change  as  an  immediate  inference ;  but  it  is  a 
question  of  little  importance. 

§  5.  There  are  two  kinds  of  immediate  inference  introduced  into 
Logic  by  Leibnitz,  which,  being  very  similar,  may  be  stated  together, — 

Added  Determinants.  The  same  mark  may  be  added  to  both  terms 
of  a  judgment.  The  new  judgment  thus  formed  is  inferred  from  the 
other.  Thus,  since  "  Coal  is  fuel,"  then  "  Cheap  coal  is  cheap  fuel ;" 
since  "  Science  is  system,"  then  "  A  false  science  is  a  false  system." 
The  extent  of  both  subject  and  predicate  is  narrowed,  is  more  closely 
determined.  This  is  thinking  in  a  mark,  going  from  genus  to  species. 
We  add  that  the  subtraction  of  the  same  determinant  from  both  sub- 
ject and  predicate  is  also  legitimate,  but  not  an  inference. 

Complex  Conceptions.  This  inference  is  parallel  to  the  other.  The 
two  terms  of  a  judgment  may  be  added  as  marks  to  the  same  concept. 


INFERENCES.  105 

Thus,  since  "  Science  is  system,"  then  "  A  scientific  arrangement  is  a 
systematic  arrangement ;"  and  since  "  Coal  is  fuel,"  then  "  The  con- 
sumption of  coal  is  the  consumption  of  fuel."  Two  judgments  may 
be  amalgamated  on  this  principle,  the  terms  of  one  being  added  as 
marks  to  the  terms  of  the  other.  Thus,  since  "  A  museum  is  a  collec- 
tion of  interesting  objects,"  then  "  A  scientific  museum  is  a  systema- 
tized collection  of  interesting  objects." 

§  6.  Inflnitation.'  This  mode  of  immediate  inference  passes  from 
the  merely  negative  judgment  to  the  infinite  judgment  of  Kant 
(i,  §  9).  It  places  the  subject  in  the  outer,  infinite  sphere  of  things, 
and  limits  it  only  by  the  subtraction  of  the  predicate  from  that 
sphere.  Thus,  from  "The  soul  is  not  mortal,"  I  immediately  infer 
that  "  The  soul  is  non-mortal."  These  propositions  express  different 
thoughts.  They  are  not  equal,  not  identical,  but  merely  similar.  The 
inverse  inference  is  included  under  the  same  name ;  i.  e.,  the  reduc- 
tion of  an  infinite  proposition  to  a  mere  negative,  is  also,  for  conven- 
ience, called  infinitation.  Thus,  from  "  Quakers  are  non-combatants," 
we  immediately  infer  that  "  Quakers  are  not  combatants."  Also 
purely  affirmative  and  doubly  negative  judgments  are  said  to  be  in- 
iinitated  thus,  since  "  Man  is  mortal,"  then  "  No  man  is  non-mortal;!* 
and  vice  versa.  Hence,  for  immediate  inference  by  infinitation,  the 
RULE  :  Change  the  quality  of  the  judgment  and  of  the  predicate. 
This  is  done,  if  the  premise  has  either  a  negative  copula  or  predicate, 
by  simply  transferring  the  negative  particle  from  one  to  the  other;  if 
both  are  negative,  by  subtracting  it  from  both ;  if  neither,  by  adding 
it  to  both.  Observe  that,  though  the  quality  of  the  judgment  is  always 
changed,  the  quantity  remains  unchanged.  This  process  Bain  calls 
"  Obversion,"  but  he  denies  that  it  is  properly  an  inference,  insisting 
that  the  two  notions  arc  mutually  implied  under  the  law  of  Relativity. 

To  avoid  awkward  compounds  with  non,  we  make  use  of  a  priva- 
tive prefix  or  suffix,  as  in-,  un-,  dis-,  -less,  etc.,  although,  as  has  been 
repeatedly  remarked,  words  so  formed  are  often  not  pure  negatives. 
For  example,  they  often  mean,  not  the  privation  of  the  quality,  but 
the  existence  of  it  in  a  low  degree ;  as,  unwise,  careless.  So  uncom- 
pounded  negative  terms  are  generally  impure  ;  as,  night,  crooked.  We 


3  Commonly  called  by  the  old  logicians  J^quipollence.  We  use  this  word,  how- 
ever, in  a  sense  more  accordant  with  its  etymology,  to  mean  the  same  thought  only 
in  a  different  phraseology.  See  Part  1st,  ii,  §  8. 


106  OF    JUDGMENTS. 

are,  then,  to  be  on  our  guard  in  using  such  terms  to  express  infinita- 
tion,  lest  we  derive  too  much.  Under  this  precaution  we  add  some 
illustrations  as  follows, — 

Since  All  metals  are  fusible ;     then  No  metal  is  infusible A  yields  E 

"      No  miser  is  happy ;  "    Every  miser  is  unhappy E      "      A 

"     Some  sins  are  pardonable ;  "     Some  sins  are  not  unpardonable. . .  I      "      O 
"     Some  men  are  not  gentle ;    "     Some  men  are  ungentle 0     "      I 

We  may  pursue  a  thought  through  a  series  of  immediate  inferences, 
as  in  the  following  example, — 

Since  Some  invisible  things  are  not  intangible ; =  0 

Then  Some  invisible  things  are  tangible ; =  I 

(Convert  simply.) 

Then  Some  tangible  things  are  invisible ; =  I 

Then  Some  tangible  things  are  not  visible =  0 

De  Morgan,  followed  by  Thomson,  Bowcn,  McCosh,  and  other  logi- 
cians, derives  this  last  directly  from  the  first  by  a  complex  rule,  and 
classes  it  as  a  second  method  of  infinitation ;  but,  as  it  obviously  in- 
volves conversion,  to  do  so  needlessly  confuses  two  modes  of  infer- 
ence. One  other  example, — 

Since  Every  unjust  act  is  inexpedient ; =  A 

Then  No  unjust  act  is  expedient ; =  E 

(Convert  simply.) 

Then  No  expedient  act  is  unjust;  —  E 

Then  Every  expedient  act  is  just =  A 

Some  moralists  who  would  contend  for  the  first  proposition  of  this  se- 
ries, would  hesitate  to  admit  the  last.  But  the  inference  is  necessary. 

§  7.  Conrersion.  In  immediate  inference  by  conversion,  the  sub- 
ject and  predicate  change  places  with  each  other ;  i.  e.,  the  terms  are 
transposed.  Besides  observing  the  general  rule  given  above  (§  3), 
we  must  take  heed  to  make  a  total  transfer ;  i.  e.,  the  whole  naked 
subject  must  be  made  predicate,  and  the  whole  naked  predicate  made 
subject.  By  a  naked  term  is  meant  a  term  without  its  sign  of  quan- 
tity, all,  some,  etc.  Thus,  from  "  Every  old  man  has  been  a  boy," 
we  cannot  infer  that  "  Every  boy  has  been  an  old  man ;"  but  only 
"  Some  one  who  has  been  a  boy  is  an  old  man."  Hence,  to  avoid 
error,  it  is  generally  needful  before  converting  to  reduce  the  proposi- 
tion to  its  strict  logical  form,  that  in  which  subject,  copula,  and  predi- 
cate distinctly  appear.  We  will  consider  only  three  kinds  of  illative 


INFERENCES.  107 

conversion,  and  these  only  so  far  as  our  subsequent  need  in  syllogiz- 
ing requires,  which  is,  that  \ve  be  able  to  convert  each  of  the  four 
judgments  A,  E,  I,  O. 

1st.  Simple  conversion  transposes  the  terms  without  changing  the 
quantity  or  the  quality  of  the  proposition.  It  may  be  applied  to  E, 
and  to  I.  Thus, — 

Since  JS"o  one  without  warm  sympathies  is  a  true  poet ; =  E 

Then  No  true  poet  is  without  warm  sympathies ; =  E 

Since  Some  good  mathematicians  are  poor  financiers; =  I 

Then  Some  poor  financiers  are  good  mathematicians =  I 

The  judgment  of  degree  (i,  §  13),  symbolized  by  A  or  E,  is  always 
and  only  simply  convertible. 

2d.  Conversion  per  accidens  reduces  the  quantity  of  a  proposition 
(hence  also  called  C.  by  limitation),  but  leaves  its  quality  unchanged. 
It  is  applied  to  A,  cud  the  converse  is  I.  Thus, — 

Since  All  plane  triangles  are  rectilinear  figures  ; —  A 

Then  Some  rectilinear  figures  are  plane  triangles =  I 

The  name  was  given  by  Boethius,  because  it  is  not  a  conversion  of 
the  universal  per  se,  but  only  of  a  particular  which  the  universal  in- 
cludes. If  we  hold  to  the  rule  that  affirmatives  do  not  distribute  the 
predicate,  it  is  evident  that  the  predicate  of  the  convertend,  "recti- 
linear figures,"  does  not  change  its  quantity  in  becoming  the  subject 
of  the  converse.  But,  for  the  same  reason,  the  subject  of  the  con- 
vertend, "  plane  triangles,"  in  becoming  the  predicate  of  the  affirma- 
tive converse,  has  its  quantification  reduced.  Also  observe  that  our 
general  rule  (§  3)  forbids  us  to  retrace  this  step — to  reconvert  the  I 
into  A.  E  also  may  be  converted  per  accidens. 

3d.  Conversion  by  contraposition  changes  the  quality  but  not  the 
quantity  of  the  proposition.  It  is  applied  to  the  remaining  judgment 
O,  and  the  converse  is  I.  In  order  to  contrapone  we  have  the  follow- 
ing RULE  :  Infinitate  and  then  convert  simply.  Thus, — 

Since  Some  pure  air  is  not  wholesome ; =  0 

Then  Some  unwholesome  air  is  pure =  I 

This  is  of  course  a  compound  process,  and  was  devised  to  convert  O, 
•which  cannot  be  converted  simply,  or  per  accidens.  It  has  been  also 
called  "  conversion  by  negation." 

Upon  a  slight  inspection  it  is  sufficiently  obvious  that  the  doctrine 
of  conversion  has  respect  to  judgments  in  extension.  An  intensive 


108      -  OF    JUDGMENTS. 

judgment  cannot  be  converted  without  at  the  same  time  changing  its 
subject  into  a  mark,  and  its  predicate  into  a  concept ;  as,  "  All  men 
are  mortal  "  converts  to  "  Some  mortals  are  human."  Otherwise  the 
view  in  converting  must  be  changed  to  extension. 

Again,  since  an  individual  cannot  become  a  predicate  (i,  §  6),  it  fol- 
lows that  no  individual  judgment  (i,  §  8)  can  be  converted.  The 
symbol  A  or  E  (i,  §  10),  when  used  to  represent  it,  must  be  held  incon- 
vertible. We  say  "Venus  is  pretty,"  and  may  say,  "Something 
pretty  is  Venus ;"  but  this  apparent  conversion  per  accidens  is  only  a 
rhetorical  inversion  ;  the  subject  of  thought  is  still  Venus.  This  gives 
occasion  to  remark  that  no  mere  inversion  is  a  logical  conversion. 

§  8.  Opposition.  A  subject  and  predicate  given  in  either  one  of 
the  four  forms  A,  E,  I,  O,  is  in  opposition  to  the  same  matter  in 
each  of  the  other  three  forms.  The  opposition  is  such  that  if  the 
given  proposition  be  taken  as  true,  or  as  false,  we  can  immediately 
infer  the  truth  or  falsity  of  at  least  some  of  the  others.  It  is  of  four 
kinds,  usually  exhibited  upon  a  diagram,  thus, — 

All  Salt  is  Pure,       \ Contrary E      No  Salt  is  Pure. 


SQUARE  OF  ;§  &  «*.  "^  OPPOSITION. 

\S  \J 

Some  Salt  is  Pure,     .  1  Subcontrary  — ! —  0    Some  Salt  is  not  Pure. 

1st.  Contradictory  opposition  exists  between  propositions  having 
the  same  naked  or  unquantified  subject  and  predicate,  but  which  dif- 
fer in  both  quantity  and  quality.  Both  cannot  be  true,  and  both 
cannot  be  false.  This  is  merely  a  specific  statement  of  the  laws  of 
Contradiction  and  Excluded  Middle.  E.  g.,  If  A,  "  All  Salt  is  Pure," 
be  sublated  (denied),  then  by  an  immediate  inference  we  can  posit 
(affirm)  O,  "  Some  Salt  is  not  Pure."  If  I,  "  Some  Salt  is  Pure,"  be 
posited,  then  we  can  immediately  sublate  E,  "  No  Salt  is  Pure."  If 
it  is  true  that  "  Every  man  has  a  conscience,"  then  it  cannot  be  said 
that  "  Some  men  have  no  conscience."  Again,  if  you  prove  that  "  A 
doctrine,  such  as  the  connection  between  mind  and  body,  is  to  be  be- 
lieved, though  it  is  not  comprehensible,"  you  have  thereby  shown  that 
"No  doctrine  is  to  be  disbelieved  because  it  is  incomprehensible." 


INFERENCES.  109 

Such  propositions  are  said,  in  common  phrase,  to  be  diametrically  op- 
posed. Aristotle  used  the  diagonal  for  the  contrary  opposition  of  A 
and  E,  and  for  this  reason,  perhaps,  the  phrase  "  diametrically  op- 
posed" is  ambiguous,  it  being  applied  both  to  contraries  and  to  con- 
tradictories.4 Contradictory  opposition  is  the  only  perfect  form  of 
opposition,  all  others  being  more  or  less  imperfect. 

Proof  is  direct  and  indirect.  If  we  wish  to  refute  an  adversary,  we 
may  show  that  his  arguments  are  false,  do  not  sustain  his  assertion, 
which,  being  unsupported,  fails.  The  result  is  merely  negative,  and  is 
often  sufficient.  But  we  may  wish  to  go  further,  and  prove  his  asser- 
tion positively  false.  If  this  is  done  by  an  attack  upon  his  own  as- 
sertion, the  method  is  direct.  But  if  we  affirm  the  contradictory 
proposition,  and,  having  established  it,  immediately  infer  his  assertion 
false,  the  method  is  indirect.  Thus,  if  one  affirms  with  Hobbes  that 
"  All  human  motives  are  always  ultimately  selfish,"  we  may  undertake 
to  prove  that "  Some  one  motive  in  some  single  case  was  unselfish." 
If  this  be  established,  then  the  immediate,  necessary  inference  from 
this  O  is,  that  his  A  is  false.  The  proof  called  reductio  ad  absurdum 
is  indirect  and  quite  similar.  Euclid  makes  much  use  of  it.  Instead 
of  demonstrating  a  proposition  directly,  he  demonstrates  that  its  con- 
tradictory is  absurd  and  thence  infers  its  truth. 

2d.  Contrary  opposition  exists  between  A  and  E,  universal  propo- 
sitions differing  in  quality  only.  Both  cannot  be  true,  but  both  may 
be  false.  Between  these  propositions  there  is  a  tertium  quid,  namely 
I  and  O.  If  A,  "  All  S  is  P,"  be  posited,  E,  "  No  S  is  P,"  is  sublated, 
and  vice  versa.  But  if  either  is  sublated,  this  does  not  posit  the  other, 
for  it  may  be  that  "Only  some  S  is  P"  — I  and  O.  To  deny  that 
"All  Stars  are  Planets"  does  not  afford  the  inference  that  "No  Stars 
are  Planets ;"  for  it  may  be,  and  in  this  case  is,  true  that  some  are, 
and  some  are  not.  To  sublate  "  No  wars  are  evil "  does  not  give  po- 
sition to  "  All  wars  are  evil ;"  for  if  some  are,  and  some  are  not,  then 
both  the  others  are  false. 

When,  however,  the  judgment  or  proposition  is  individual,  all  dis- 

4  The  Aristotelic  doctrine  of  Opposition  differs  considerably  from  the  one  here 
given,  which  is  the  approved  Scholastic  form.  Saint-Hilaire  represents  the  former 
thus:  " L'opposition  (TO.  avriKiifj^va)  peut  etre  de  quatre  espeees.  II  y  a:  1° 
celle  des  relatifs ;  2°  celle  des  contraires ;  3°  celle  de  la  privation  et  de  la  posses- 
sion (TiprjmQ  ical  t£ic) ;  4°  enfin  celle  de  1'affirmation  et  de  la  negation.  Cette  the- 
orie  des  oppositions  joue  un  grand  role  dans  le  systeme  d'Aristote." — De  la  Lo- 
giqm  D'Aristote,  Tome  i,  p.  172  sq.  (Paris,  1838).  See  Aristotle's  Categories,  ch.  x. 


110  OF    JUDGMENTS. 

tinctions  in  opposition  disappear,  or  rather  become  merged  into  the 
simple  negative,  which,  in  such  case,  is  the  true  contradictory.  E.  g., 
"  Caliban  is  a  man,"  and  "  Caliban  is  not  a  man." 

In  controversy  opponents  often  take  contrary  positions,  and  either 
failing  to  establish  his  own  gives  to  the  other  an  apparent  victory. 
E.  g.,  One  asserts  that  "  All  men  are  to  be  trusted."  Another  opposes 
this  with  "  No  men  are  to  be  trusted,"  but  being  unable  to  prove  it  in 
face  of  cited  cases  of  some  who  are  to  be  trusted,  leaves  the  question 
in  confusion,  and  his  opponent  in  possession  of  the  field.  Indeed, 
they  have  not  squarely  faced  each  other.  The  opposer,  in  adopting 
the  indirect  method,  should  have  undertaken,  not  the  contrary,  which 
is  too  much,  but  the  diametrical  contradictory,  that "  Some  men  are 
not  to  be  trusted,"  which  in  this  case  would  insure  an  easy  victory. 

3d.  Subcontrary  opposition  exists  between  I  and  O,  particular  prop- 
ositions differing  in  quality  only.  Both  may  be  true,  but  both  cannot 
be  false.  Hamilton  calls  these  subaltern  contraries,  "  compossible." 
If  I,  "  Some  S  is  P,"  be  taken  as  true,  it  may  be  that  0,  "  Some  S  is 
not  P,"  is  also  true.  But  if  I  is  false,  then  O  must  be  true.  If  "  Some 
Sighs  are  Prayers,"  it  may  also  be  true  that  "  Some  Sighs  are  not 
Prayers."  But  if  it  is  false  to  say  that  "  Some  Sighs  are  Prayers," 
then  it  must  be  true  that  "  Some  are  not." 

Let  it  be  noticed,  however,  that  if,  in  "  Some  S  is  P,"  and  "  Some  S 
is  not  P,"  the  same  "Some"  is  intended,  then  the  propositions  are  "in- 
compossible."  In  strictness  they  become  contraries,  and  hence  pure 
Logic,  which  takes  it  thus,  knows  no  subcontrary  opposition.  But 
usually  the  sphere  of  the  "  Some  "  in  the  one  is  different  from  that 
in  the  other.  Thus,  if  I  observe  that  "  Some  metals  (some  at  least, 
perhaps  all)  are  fusible,"  it  may  be  that  "  Some  others,  for  aught  I 
know,  are  infusible."  Here  the  "  Some  "  is  wholly  indefinite,  and  our 
rule  holds  good.  But,  further,  if  the  "  Some  "  be  thought  as  semi- 
definite  (i,  §  8),  then  our  rule  changes  from  "  Both  may  be  true  "  to 
"  Both  must  be  true."  Thus,  I  know  that  "  Some  flowers  (some  at 
most,  not  all)  are  fragrant ;"  then  it  must  be  true  that  "  Some  flowers 
are  not  fragrant."  This  Hamilton  calls  "integration,"  since  the  two 
"  Somes,"  taken  together,  constitute  the  whole. 

4th.  Subalternate  opposition  exists  between  propositions  differing 
in  quantity  only.  If  the  universal  is  true,  the  particular  is  true ;  if 
the  particular  is  false,  the  universal  is  false.  If  I  have  $100  at  my 
credit  in  bank,  it  is  evident  I  may  draw  for  $5  or  $10.  If  I  have  not 
$10  at  my  credit,  I  cannot  draw  $100.  This  is  a  specific  application 


UK1 


INFERENCES. 

of  the  law  of  Identity.  If  it  is  true  that "  All  Sin  must  be  Punished," 
then  we  can  infer  that  "  Some,  or  any  one,  Sin  must  be  Punished."  If 
"Some  Sin,  even  one,  will  not  be  Punished"  be  proved  false,  than  _ 
we  cannot  say  that  "  No  Sin  will  be  Punished."  The  reverse  of  the 
rule,  however,  does  not  hold.  From  "  Some  S  is  P,"  it  does  not  fol- 
low that  "  All  S  is  P."  If  "  No  S  is  P  "  is  a  false  statement,  we  can- 
not infer  that  "  Some  S  is  P  "  is  also  false.  Though  to  say  that  "  No 
Subjects  can  become  Predicates  "  is  untrue,  still  it  is  true  that  "  Some 
Subjects,  as  individuals,  cannot  become  Predicates." 

An  exception  is  to  be  taken  also  here.  If  a  particular  proposition 
is  thought  as  semi -definite,  it  follows  that  the  universal  is  false. 
If  "  Only  some  flowers  are  fragrant,"  I  and  O,  then  it  is  false  to  say 
either  that  "  All  are,"  or  that  "  None  are."  Also,  if  a  universal  is 
true,  then  its  subalternate  particular  is  false.  If  "  All  Scripture  is 
Profitable,"  then  we  cannot  think  that  "  Some  (some  at  most,  not  all) 
Scripture  is  Profitable."  If  we  accept  that  "  No  Scripture  should  be 
Profaned,"  then  we  cannot  consistently  think  that  "Some  (some  only) 
Scripture  should  not  be  Profaned."  In  semi-definite  thought  the  rule 
for  subalternate  opposition  becomes  "  If  either  is  true,  the  other  is 
false."  This  modified  form  of  the  opposition  Hamilton  calls  "  incon- 
sistency.5 

Let  us  repeat  here  an  exceptive  remark  made  above,  that  individual 
propositions  have  only  one  opposite.  The  subject  being  an  individual 
total,  its  quantity  cannot  be  reduced.  Hence  there  is  no  subaltern, 
nor  diagonal  contradictory.  The  simple  contrary  or  negative  is  a 
complete  contradiction.  E.  g.,  "  Diogenes  was  a  fool,"  and  "  Diogenes 
was  not  a  fool." 

The  relation  between  subcontraries,  as  well  as  that  between  subal- 
terns, is  not  strictly  opposition.  Between  subcontraries  there  is  no 
real  contrariety,  but  rather  a  presumption  of  agreement,  a  presumption 
that  both  are  true.  Between  subalterns  the  relation  is  that  of  a  par- 
tial agreement,  or  subordination,  which  Hamilton  calls  "  restriction." 
But  for  convenience  and  brevity,  logicians  treat  them  as  species  under 
opposition.6 

5  Lor/ic,  pp.  530-535.     Aristotle  never  recognizes  the  semi-definite  judgment. 
With  him  a  particular  proposition  is  always  construed  as  wholly  indefinite. 

6  Aristotle  does  not  mention  subalternate  opposition.     He  names  subcontrary 
opposition,  but  declares  it  to  be  merely  verbal,  not  real.     He  speaks  of  contra- 
dictories as  opposites  (ai>riKe<'/i6vat),  apparently  considering  these  alone  as  really 
opposed.     Sec  Waitz,  Comment,  on  Organ,  lib  16.     Cf.  Cic.  Top.  xi,  §  47. 


112  OF   JUDGMENTS. 

4 

The  chief  results,  not  including  the  semi-definite  meaning,  may  be 
summed  as  follows, — 

All  S  is  P,  "I 

Some  S  is  not  P. 

}-  Contradictories : — One  must  be  true,  and  the  other  false. 
No  S  is  P, 

Some  S  is  P.        J 

N    S  '^  P'  f  Contraries : — Both  cannot  be  true,  but  both  may  be  false. 

'    T.   f  Subcontraries : — Both  may  be  true,  but  both  cannot  be  false. 
Some  S  is  not  P.  ) 

All  S  is  P,  -] 

Some  S  is  P. 


i  S  b  It        tes  • •$  ^  ^e  uniyersal  ig  ^rue>  *ne  particular  is  true ; 

Some  S  is  not  P. 

The  same  matter  may  be  tabulated  also  thus, — 


No  S  is  P  I  If  the  particular  is  false,  the  universal  is  false. 

\] 


Contradictories.    Contraries.    Subalterns, 
r  If  A  is  true,    0  is  false, E  false,  —  I  true. 

If  E  is  true,    I  is  false, A  false, 0  true. 

Umversals  •<  _.  .  .    „  .       _  .    A         , 

If  A  is  false,  0  is  true.   )  The  otherg  undetermined. 

v.  If  E  is  false,  I  is  true.   ) 

,  If  I  is  true,  E  is  false.  )  The  otherg  undeterminedi 
If  0  is  true,  A  is  false.  ) 


Particulars  -j 

If  0  is  false,  A  is  true, I  true,  . . . .  E  false. 


i  If  I  is  false,  E  is  true, 0  true, A  false. 


Hence  by  the  truth  of  universals,  and  by  the  falsity  of  particulars,  all 
others  are  determined ;  otherwise  only  the  contradictory.6 

•        v 

*  The  old  Latin  logicians  rather  needlessly  warn  us  that  opposition  cannot  be 
correctly  said  to  exist  unless  the  predicate  [and  the  subject]  of  both  propositions 
is  truly  the  same.  We  violate  this  precaution,  say  they,  when  we  do  not  predicate 
in  the  same — 

1.  Manner;  as,  Hector  is  and  is  not  a  man;  i.  e.,  he  is  a  dead  man,  but  not  a 

living  one. 

2.  Respect;  as, Zoilus  is  and  is  not  black;  i.e.,  he  is  black-haired,  but  red- 

faced. 

3.  Degree ;  as,  Socrates  is  and  is  not  long-haired ;  i.  e.,  he  is,  compared  with 

Scipio,  but  not,  compared  with  Xenophon. 

4.  Time ;  as,  Xestor  is  and  is  not  an  old  man ;  i.  e.,  he  is  not  when  a  boy,  but 

is  at  the  siege  of  Troy. 


INFERENCES.  113 

§  9.  Praxis.     Draw  an  immediate  inference  from  each  of  the  fol- 
lowing propositions  by  added  determinants  (§  5) : — 

1.  The  wages  of  sin  is  death. 

Use  as  determinants, — inevitable,  and  just. 

2.  Novelty  is  pleasure. 

Use  as  a  determinant, — the  greater  the. 

3.  War  is  an  evil. 

Use, — unprovoked,  welcomed   with  ardor,  which  reaches   to  our 
hearth-stones. 

Infer  from  the  following  by  complex  conceptions  (§  5) : — 

4.  The  ignorant  are  ceremonious. 
Use  the  concept, — an  age. 

5.  Heaven  from  all  creatures  hides  the  book  of  fate. — Pope. 
Use, — wisdom  and  love. 

V- 

Combine  each  of  the  following  pairs  into  one  proposition  (§  5)  : — 

C.  Honesty  deserves  reward. 

Every  man  whom  we  meet  is  a  neighbor. 

7.  The  year  is  dying  in  the  night. — Tennyson. 
The  swift  runner  is  speedily  exhausted. 

Infinitate  each  of  the  following  propositions  (§  6) : — 

8.  All  knowledge  is  useful. 

9.  The  Chinese  are  industrious. 

10.  No  reptiles  have  feathers. 

11.  It  is  wrong  to  put  an  innocent  man  to  death. 

12.  There  are  studies  much  vaunted,  yet  of  little  utility. 

13.  Some  men's  hearts  are  not  in  the  right  place. 

14.  In  jewels  and  gold,  men  cannot  grow  old. 

15.  No  brutes  are  responsible. 

Convert  each  of  the  following,  affixing  the  symbols  (§  7)  : — 

16.  Life  every  man  holds  dear. 

17.  Two  straight  lines  cannot  enclose  a  space. 

1 8.  None  are  free  who  do  not  govern  themselves. 

19.  With  man  many  things  are  impossible. 

20.  Few  know  themselves. 

21.  'Tis  cruelty  to  load  a  falling  man. 

22.  Fame  is  no  plant  that  grows  on  mortal  soil. 

8 


114  OF   JUDGMENTS. 

23.  Whoso  loveth  instruction,  loveth  knowledge. 

24.  Each  mistake  is  no  proof  of  ignorance. 

25.  Fair  promises  are  often  not  to  be  trusted. 

26.  There  falls  no  shadow  on  his  tomb. 

27.  Full  many  a  gem  of  purest  ray  serene, 

The  dark  unfathomed  caves  of  ocean  bear. — Gray. 

From  each  of  the  following  premises  obtain,  by  immediate  infer- 
ences, the  annexed  conclusion  (§§  6  and  7) : — 

28.  All  the  righteous  are  happy ; 

.'.  Whoever  is  unhappy  is  wicked. 

29.  No  human  virtues  are  perfect ; 

.".  All  perfect  virtues  are  superhuman. 

30.  Some  possible  cases  are  improbable ; 

.*.  Some  improbable  cases  are  not  impossible. 

31.  Some  true  patriots  are  not  popular; 

.'.  The  unpopular  are  not  always  unpatriotic. 

32.  Certainty  is  a  kind  of  light ; 

/.  Darkness  is  doubt. 

If  the  following  propositions  are  true,  what  opposites  arc  also  true, 
and  what  false  ?  (§  8)  :— 

33.  By  night  an  atheist  half  believes  a  God. —  Young. 

34.  No  one  is  always  happy. 

35.  Some  democracies  are  unstable. 

36.  Some  great  orators  are  not  statesmen. 

If  the  following  are  false,  what  opposite  propositions  arc  also  false, 
and  what  true  ?  (§  8) : — 

37.  All  self-confident  persons  have  strong  will. 
3£.  No  honest  men  become  bankrupt. 

39.  Some  private  vices  are  public  benefits. 

40.  Some  plants  do  not  produce  seed. 


INNOVATIONS.  115 


III.  INNOVATIONS. 

§  1.  Since  the  revival  in  England  of  the  study  of  Logic,  which  was 
brought  about  by  the  publication  of  Whately's  treatise,  there  has  been 
manifested  much  dissatisfaction  with  the  Aristotelic  doctrines  as  in- 
herited from  the  scholastic  or  Latin  logicians  of  the  Middle  Ages. 
This  body  of  doctrine  we  have  spoken  of  as  the  old,  or  Latin  Logic, 
not  meaning  to  intimate  thereby  that  it  is  obsolete,  or  even  likely  to 
vanish  away,  but  simply  to  distinguish  it  from  recent  doctrines.  The 
dissatisfaction  has  arisen  not  so  much  from  a  supposed  inaccuracy  of 
the  old  doctrines  as  from  their  supposed  inadequacy.  Many  impor- 
tant modifications  and  additions  have  been  proposed  by  high  authori- 
ties, such  as  Hamilton,  De  Morgan,  Mansel,  Boole,  Thomson,  Mill, 
Bain,  Jevons,  and  others,  but  as  yet  few  have  been  generally  accepted, 
and  the  old  Logic  holds  its  ground.  Hamilton  has  been  the  chief 
innovator,  his  views  have  been  most  widely  discussed,  and  made 
the  deepest  impression ;  and,  therefore,  we  will  give  our  attention  es- 
pecially to  them. 

§  2.  Hamilton's  doctrine  of  the  semi-definite  "  Some"  has  already 
been  stated/  But  it  is  very  questionable  whether  it  should  be  re- 
ceived into  Logic  at  all,  even  as  a  mere  exception.  "  Some,"  if  not 
wholly  and  simply  indefinite,  probably  always  designates  either  a 
wholly  definite  judgment  imperfectly  expressed,  or  else  a  compound 
judgment  whose  two  elements  are  each  wholly  indefinite.  If  we  say 
"  Some  members  of  this  University  are  now  studying  Logic,"  this 
judgment  in  our  minds  would  be  wholly  definite,  a  certain  "  Some,"  i.  e., 
"All  the  members  of  the  Philosophy  Class  are  now  studying  Logic," 
without  any  thought  whatever  of  other  members  of  the  University. 

1  In  i,  §  8.  It  may  be  remarked  that,  if  fully  adopted,  its  consequence  to  the  old 
doctrine  of  Opposition  (ii,  §  8),  enlarged  by  the  addition  of  four  judgments,  is  some- 
thing fearful.  The  student  is  referred  to  the  tabulated  statement  in  the  Appendix 
to  Hamilton's  Logic,  p.  535,  where  the  whole  scheme  is  elaborately  worked  out. 
Instead  of  thus  replacing  entirely  the  old  doctrine  of  Opposition  with  the  new  one 
of  "Incompossibility,"  it  would  seem  simpler  and  sufficient,  and  hence  better,  to 
treat  the  cases  of  the  semi-definite  meaning  as  exceptions  to  the  old  rules. 


116  OF    JUDGMENTS. 

The  judgment  then  is  A,  and  the  proposition  should  be  reduced  to 
that  form,  in  conformity  with  the  thought.  Again,  if  we  say  "  Some 
flowers  are  fragrant,"  meaning  "  some  at  most,  not  all,"  then  this  im- 
plies the  counter-thought  that  "Some  flowers  are  not  fragrant."  If 
this  double  thought  be  expressed  in  a  grammatically  simple  sentence, 
for  the  logician  postulates  that  it  be  expressed,  then  we  have  "  Only 
some  flowers  are  fragrant."  This  is  an  exponible  compound  proposi- 
tion which  analyzes  into  "  Some  flowers  (I  know  not  how  many)  are 
fragrant"  (I),  and  "Some  flowers  (I  know  not  how  many)  are  not 
fragrant"  (0).  Each  of  these  elements  considered  in  itself,  entirely 
apart  from  the  other,  is  wholly  indefinite ;  for  the  meaning  of  "  I 
know  not  how  many"  must  in  that  case  be  "perhaps  all."  The 
semi-definite  character  does  not  at  all  appear  unless  one  judgment  is 
recognized  as  limiting  the  other ;  and  when  this  is  the  case  the  judg- 
ment is  not  simple,  but  compound.  Now  Logic,  professing  to  be  n 
thorough  analysis  of  thought,  must  not  stop  short  of  its  simple  ele- 
ments, must  not  recognize  the  compound  as  co-ordinate  with  the  sim- 
ple, and  does  not,  cannot,  undertake  to  formulate  the  compound  modes 
of  thought,  which  are  legion,  but  evolving  their  elements  formulates 
only  these.  Therefore  the  semi-definite  judgment,  being  compound, 
must  be  denied  a  position  among  the  elementary  forms  of  thought, 
and  if  recognized  at  all  must  take  its  place  among  the  abbreviated,  im- 
perfect modes  of  statement,  subject  at  any  moment  to  analysis  and 
full  discrete  expression. 

§  3.  The  most  important  addition  to  the  old  Logic  proposed  by 
Hamilton  is  his  doctrine  of  "The  Thorough-going  Quantification  of 
the  Predicate."8  The  old  Logic  teaches  that  negatives  distribute  the 
predicate,  affirmatives  do  not  (i,  §  9).  Hamilton  teaches  that  in 
both  affirmative  and  negative  judgments  the  predicate  may  be  either 
distributed  or  undistributed.  Hence,  to  the  four  Aristotelic  judg- 
ments of  the  old  Logic  he  has  superadded  four  others,  commonly 

2  See  Hamilton's  Logic,  Appendix,  p.  509  sq.  As  Bacon  called  bis  great  work 
the  Novum  Oryanum,  in  allusion  to  the  Aristotelic  Oiyanon,  so  Hamilton  calls  his 
treatment  of  these  for.ms  the  "  New  Analytic,"  in  allusion  to  Aristotle's  "  Analytics," 
and  proposes  thereby  "  to  place  the  keystone  in  the  Aristotelic  arch."  For  an  ex- 
cellent statement  of  Hamilton's  views,  warmly  approved  by  himself,  see  An  Essay 
on  the  New  Analytic  of  logical  Forms,  by  Thomas  Spencer  Baynes,  an  admiring 
pupil  of  Hamilton's.  The  Essay  is  the  more  interesting  from  having  been  a  prize 
examination  paper. 


INNOVATIONS. 


117 


called  the  Ilamiltonian  judgments.     These  are  included  in  the  fol- 


lowing- table. 


TABLE  OF  THE  EIGHT  PROPOSITIONAL  FORMS. 


BEST 


Aff. 


WORST 


1,  u,  afa,  Toto-total,      All  men  are  all  reasoners |mcn  C: »-  :P 

lovers 

—  ii,  A,  afi,    Toto-partial,   All  men  are  some  lover? [men  £:  ^  ^ 

poets 

— 3,  Y,  ifa,  Parti-total,      Some  men  are  all  poets [tm?n  (^  ,^_  .p 

singers 

plv,  I,  ifi,    Parti-partial,  Some  men  are  some  singers |me"  C,  — -  ,P 

s'ngers 

U  5,  w,  ini,  Parti-partial,  £owe  men  are  not  some  singers.    lnc»  C,  BT-  ,P 

poets 

—  vi,0,  ina,  Parti-total,     Some  men  are  not  any  poets. . .    me»  C,  »K  :P 

lovers 

—  7,?;,  ani,  Toto-partial,  Not  any  men  are  some  lovers..    meu  £:••-, P 

brutes 
—  viii,  E,  ana,  Toto-total,     Not  any  men  are  any  brutes.. .    mea  C:  H-  :P 


Some  explanation,  preparatory  to  discussion,  is  needed.  The  table 
consists  of  six  columns  of  symbols,  and  one  of  examples.  All  the 
symbols  in  any  one  horizontal  line  mean  the  same  thing.  In. the  first 
column,  the  Roman  numerals  designate  the  Aristotelic  or  Latin  judg- 
ments ;  the  Arabic  numerals,  the  Hamiltonian  judgments.  In  the  sec- 
ond column,  the  Hamiltonian  judgments  also  are  designated  by  vowel 
letters :  u  for  universal ;  Y,  as  cognate  to  I ;  u>  and  77,  as  the  Greek 
correlatives  of  O  and  E.  In  the  third  column,  a  stands  for  a  univer- 
sal or  distributed  term ;  i  for  a  particular  or  undistributed  term ; 
f  (affirmo)  stands  for  the  affirmative  copula  ;  n  (ncyo)  for  the  negative 
copula  —  f  and  n  being  respectively  the  first  consonant  in  each  of 
those  words.  The  fourth  column  needs  no  explanation ;  but  we  ob- 
serve that  its  symbols  are  defective  in  not  distinguishing  the  affirma- 
tive from  the  negative  forms,  and  must  therefore  be  supplemented  by 
the  words  "affirmation"  or  "negation."  The  fifth  column  is  of  ex- 
amples, in  which  it  is  understood  that  "men"  includes  both  males 
and  females ;  and  further  that  "  birds"  for  instance,  are  " lovers"  of 
each  other,  and  also  are  " singers"  The  sixth  column  is  the  linear 
notation,  already  described  under  a  previous  topic. 


118  OF    JUDGMENTS. 

The  seventh  column  calls  for  more  remark.  It  is  an  ingenious  de- 
vice of  Hamilton's,  to  which,  however,  he  gave  no  specific  name.  As 
it  is  not  properly  symbolic,  we  will  call  it  the  "Graphic  Notation" 
The  subject  or  predicate  is  expressed  by  C  or  T  (gamma),  the  third 
letters  respectively  of  the  Roman  and  Greek  alphabets.  These  are 
taken  that  they  may  be  indifferent,  no  unconscious  preference  being 
given  to  cither,  which  perhaps  might  not  be  if  they  were  successive 
letters  from  the  same  alphabet.  The  distribution  of  either  term  is  ex- 
pressed by  a  colon  standing  next  to  it ;  thus  C:  is  read  "  All  C."  The 
non-distribution  of  cither  term  is  expressed  by  a  comma  next  to  it ; 
thus  ,F  is  read  "  Some  T."  The  positive  copula  is  expressed  by  a  point- 
ed dash  («^) ;  the  negative  by  the  same  crossed  (H-).  The  peculiar 
advantage  of  the  device  is  that  it  discriminately  expresses  either  exten- 
sion or  intension.  Pointing  to  the  predicate,  this  copula  indicates 
an  extensive  judgment,  and  should  therefore  be  read  "  contained 
under;"  thus  C:-^,F  is  read  "All  C  is  contained  under  some  F." 
Pointing  to  the  subject,  it  indicates  an  intensive  judgment,  being  read 
"  comprehends ;"  thus  C:  —  ,P  is  read  "  All  C  comprehends  some  r." 
Other  examples  are:  F,  —  ,C:=Some  T  is  contained  under  some  C; 
C:-H:P=rNot  any  C  is  contained  under  any  T;  JT, -H:C  =  Some  I1 
does  not  comprehend  any  C. 

The  meaning  of  "Best"  and  "  Worst"  in  the  table  is  this:  We 
declare  "best"  when  we  affirm  all  of  all ;  we  declare  "worst"  when 
we  deny  any  of  any.  Each  of  the  judgments  in  the  table  declares 
"  a  worse  relation  between  two  terms  than  any  that  stands  above  it." 
The  remaining  points  require  no  explanation. 

§  4.  The  first  question  before  us  is,  Whether  the  four  judgments,  u, 
Y,  w,  and  77,  are  not  such  as  the  mind  forms  and  uses,  even  though  it 
may  rarely  or  never  express  some  of  them?  True  the  predesigna- 
tions  all,  some,  any,  occurring  in  the  above  table  as  quantifying  the 
predicate,  are  not  usually  so  expressed.  Still,  in  the  old  forms  we  are 
said  to  think  in  a  quantification  for  the  predicate.  Thus  in  A,  we 
think  "  All  are  some  ;"  in  O,  "  Some  are  not  any,"  etc.  Now,  do  we 
not  also  sometimes  think  "  All  are  all,"  "  Some  are  all,"  "  Some  are 
not  some,"  and  "  Not  any  are  some?" 

The  evidence  in  favor  of  the  natural  and  common  use  of  afa,  "  All 
are  all,"  seems  to  be  overwhelming.  If  we  inquire  into  the  quantity 
of  the  predicate,  we  shall  find  that  this  is  the  form  whenever  a  prop- 
erty is  predicated;  thus,  "Man  is  risible"  means  "Man  is  all  that  is 


INNOVATIONS.  119 

risible."  So,  "  Animals  arc  sentient."  Again,  definition  seems  to  have 
this  quantity;  thus,  "Copperas  is  sulphate  of  iron"  means  "Copperas- 
is  all  sulphate  of  iron,"  or  "  All  sulphate  of  iron  is  all  copperas."  Again, 
every  exhaustive  division  yields  a  judgment  in  this  form ;  thus,  "  An- 
gles are  right  and  oblique"  means  "  Angles  are  all  right  and  oblique;" 
"  Length,  breadth,  and  thickness  are  all  the  dimensions  of  extension ;" 
"  Mankind  are  all  men  and  women ;"  "  Pompey,  Crassus,  and  Ca3sar 
were  all  of  the  first  triumvirate." 

The  form  of  a  judgment  Becomes  ifa  whenever  the  "  Some"  of  the 
subject  is  thought  as  exhausting  the  predicate ;  as,  "  Some  of  the  Class 
arc  (all  of  the)  absent ;"  "  Some  inspired  men  were  (all  of  the)  apos- 
tles ;"  "  Some  stars  are  all  the  planets."  This  appears  to  be  predicat- 
ing species  of  genus,  which  Aristotle  docs  not  provide  for  in  his  doc- 
trine of  the  predicables.  Perhaps  he  overlooked  that. 

Surely,  then,  no  one  will  deny  that  judgments  in  which  the  predi- 
cate is  thought  as  "  all"  are  natural  and  in  the  commonest  use.  "  The 
only  wonder  is,  how  they  could  have  been  almost  universally  rejected 
by  logicians  for  over  two  thousand  years,  down  to  the  time  of  Sir 
William  Hamilton."3  Since  his  day  they  have  been  accepted  and  in- 
corporated into  Logic  by  Manscl,  Baynes,  Thomson,  Jevons,  Bowen, 
and  many  others. 

The  form  ani,  it  is  said,  is  implied  whenever  genus  is  predicated  of 
species ;  for  when  we  say  a  All  are  some"  (i.  e.,  one  part  of  the  genus), 
the  law  of  Excluded  Middle  compels  us  to  think  "All  are  not  some" 
(i.  e.,  the  other  part).  If  "  All  men  are  some  animals,"  then  "  Not 
any  men  are  some  (other)  animals."  "  No  spaniel  is  some  dog  (cur)." 

The  law  of  division,  that  the  members  must  exclude  each  other, 
compels  us,  it  is  said,  to  think  the  form  ini;  i.  c.,  "Some  (crone 
species)  are  not  some  (=any  co-ordinate  species)."  E.  g.,  "  Some  trees 
(pines)  are  not  some  trees  (oaks)." 

In  general,  it  has  been  said  that  any  limiting  adjunct  qualifying 
the  predicate  is  equivalent  to  particular  quantification.  E.  g.,  "  A  rose 
is  a  fragrant  (=some)  flower"  (afi).  Likewise,  "A  rose  is  not  a 
poisonous  (=rsome)  flower"  (ani).  And  to  say  "Some  roses  are  not 
red"  is  to  say  "Some  roses  are  not  red  (=some)  roses"  (ini). 

The  consequence  to  Logic  of  this  doctrine  of  the  thorough-going 
quantification  of  the  predicate  appears,  at  the  outset,  to  be  a  simpli- 
fication, and  therefore  advantageous.  The  distinction  between  sub- 

8  Bowen's  Logic,  p.  133. 


120  OF   JUDGMENTS. 

ject  and  predicate  ceases,  it  is  claimed,  to  be  of  any  moment.  Each 
term  quantified,  it  becomes  indifferent  which  stands  first,  every  judg- 
ment being  reduced  to  an  equation  or  non-equation  of  two  terms. 
Consequently  the  old  doctrine  of  Conversion  is  swept  away,  and  we 
simply  transpose  the  quantified  terms  at  will.4  Upon  this  we  may  re- 
mark at  once,  that  to  claim  that  the  distinction  between  the  subject, 
that  which  we  are  speaking  of,  and  the  predicate,  that  which  we  say 
of  it,  has  been  reduced  to  naught,  is  absurd;  for  to  nullify  this  dis- 
tinction would  require  not  a  mere  remodelling  of  technical  forms,  but 
a  remodelling  of  the  forms  of  human  thought. 

But  we  will  concede  that  the  two  affirmative  Hamiltonian  judg- 
ments (whatever  may  be  said  of  the  negative)  occur  in  thought,  and 
appear  in  our  reasonings.  This  alone,  however,  does  not  entitle  them 
to  a  position  in  Logic  co-ordinate  with  the  Aristotelic  forms.  Before 
deciding  upon  this  claim  it  is  needful  to  re-examine  them  all  some- 
what more  closely. 

§  5.  The  second  question,  to  be  decided  affirmatively  before  the 
Hamiltonian  can  be  admitted  to  rank  with  the  Aristotelic  forms,  is, 
Are  they  simple  judgments  ?  We  undertake  to  show  that,  if  logical, 
they  are  not  simple,  but  compound,  and  hence  are  to  be  rejected. 

The  two  negative  forms,  ani  and  ini,  have  been  rejected  by  nearly 
all  logical  writers  on  various  grounds.  They  at  once  excite  prejudice 
by  being  so  awkward,  and  so  unlike  the  common  forms  of  speech. 
Says  Thomson,  "They  have  the  semblance  only,  and  not  the  power, 
of  a  denial."  We  add,  that  a  denial  is  essentially  an  exclusion ;  and 
an  exclusion,  if  the  quantity  of  the  thing  excluded  be  thought  of  at 
all,  is,  ex  m  termini,  of  a  total.  A  partial  exclusion  is  meaningless,  or 
rather  a  self-contradictory  phrase.  The  exclusion  of  a  part  of  a  thing 
has  meaning,  and  it  is,  that  the  total  portion  is  totally  excluded.  Let 
it  be  remarked  that  a  total  exclusion  (a  tautological  phrase)  is  differ- 
ent from  the  exclusion  of  a  total.  Moreover,  we  may  totally  exclude, 
and  in  simple  judgment  do  totally  exclude,  without  any  thought  what- 
ever of  the  quantity  of  the  thing  excluded.  Therefore,  no  simple  neg- 
ative judgment  can  have  a  particular  predicate. 

If  it  be  said  that  the  exclusion  of  a  part  implies  the  non-exclusion 
of  another  part,  and  that  this  is  expressed  by  ni,  we  reply  that  such  a 
proposition  is  compound,  consisting  of  a  simple  negative,  totally  ex- 

4  Hamilton's  Logic,  p.  525. 


INNOVATIONS.  121 

eluding,  arid  of  a  simple  affirmative,  including.  Such  compound 
judgments  are  admitted  to  be  conceivable,  they  may  be  sometimes 
useful,  they  may  occur  in  reasoning,  they  may  appear  as  premises  in 
syllogistic  forms.  But,  being  compound,  they  cannot  claim  a  place 
in  Logic,  much  less  can  £hey  take  rank  with  the  simple  forms,  to 
which  they  are  themselves  reducible,  and  to  which  they  must  be  re- 
duced in  any  complete  logical  analysis. 

The  form  ifa  has  been  accepted  by  some  logicians.  It  is  at  least 
very  questionable.  When  we  say  "  Some  men  are  poets,"  the  simple 
meaning  is  that  "  Some  men  are  contained  under  the  class  *  poets,' " 
or,  changing  to  intension,  that  "  Some  men  are  poetical."  In  neither 
case,  in  this  simple  predication,  does  there  seem  to  be  any  thought 
whatever  of  quantity  in  the  predicate.  It  is  neither  "all  poets  "nor 
"  some  poets."  The  quantity  is  indefinite  in  an  absolute  sense,  i.  e., 
it  does  not  exist  in  the  thought.  If  the  question  arises,  we  think  in- 
stantly that  "  All  poets  are  men,"  and  compounding  the  two  proposi- 
tions for  the  sake  of  brevity,  we  may  say,  "  Some  men  are  all  poets  " 
(—ifa).  This,  then,  also  appears  to  be  a  compound  proposition. 

I  maintain  here  that  the  predicate  of  an  affirmative,  as  well  as  of 
a  negative,  has  strictly  no  quantification  whatever.  That  assigned  by 
the  old  Logic  is  merely  in  view  of  conversion,  it  has  no  other  rele- 
vance, and  is  given  solely  in  anticipation  of  the  converse.  Now  a 
term  which  is  thought  without  reference  to  quantity  cannot  in  be- 
coming the  subject  of  an  affirmation  (unless  another  judgment  in- 
trudes) be  anything  other  than  the  wholly  indefinite  "Some"  (—  may 
be  next  to  none,  or  perhaps  all).  Hence  the  scholastic  rule  that  the 
predicate  of  affirmatives  is  (in  view  of  conversion)  undistributed ;  and 
therefore  also  A  converts  in  thought  into  I,  if  the  judgments  be  sim- 
ple ;  and  the  rule  per  accidens  cannot  be  swept  away  by  any  logical 
device.  For  true  Logic  is  not  a  juggling  with  words,  objectively,  to 
see  what  may  be  done  with  them,  but  a  representation  of  what  occurs 
subjectively  in  our  thoughts.6 

But  the  stronghold  of  Hamilton's  doctrine  is  afa.  If  this  falls,  all 
the  others  go  with  it.  Let  us  observe  that  the  doctrine  of  a  quantified 
predicate,  either  old  or  new,  is  applicable  only  to  judgments  in  extcn- 

8  Let  us  note,  by  anticipation,  that  in  the  syllogistic  rule  requiring  that  the  mid- 
dle term  be  distributed  at  least  once,  we  are  usually  warned  that  the  predicates  of 
affirmatives  are  "  undistributed."  It  should  be,  are  "  not  distributed,"  a  pure  neg- 
ative, meaning  less  than  "  undistributed,"  which  is  equivalent  to  "  particular." 


122  OF   JUDGMENTS. 

sion.  We  can  sec  a  good  reason  for  thinking  a  quantity  into  the 
predicate  in  anticipation  of  conversion,  as  in  the  old  doctrine ;  but  to 
hold  with  Hamilton  that  the  predicate  is  always  quantified  in  thought 
is  to  exclude  the  judgments  in  intension  from  Logic.  But,  by  a  curi- 
ous inconsistency,  he,  more  than  any  other  logician,  insists  upon  inten- 
sion, and  expands  Logic  to  embrace  it  fully.  One  of  the  two,  how- 
ever, must  be  given  up.  But,  if  we  give  up  intension,  we  must  give  up 
extension  also,  for  intension  is  primary,  and  then  Logic  ceases  to  be. 
Says  Mill,  "Propositions  in  extension  have  absolutely  no  meaning 
but  what  they  derive  from  comprehension.  The  Logic  of  the  quanti- 
fied predicate  takes  the  comprehension  out  of  them,  and  leaves  them 
a  caput  mortuum"  This  consequence  is  certainly  sufficient  to  cast  a 
shade  of  suspicion  over  the  well-fortified  afa. 

When  we  make  the  assertion  that  "All  triangles  arc  all  trilaterals," 
is  it  not  evident  that,  to  cover  the  whole  ground  occupied  by  this 
statement,  two  judgments  are  required:  first,  that  "Every  triangle  is 
trilateral,"  and,  secondly,  that  "  Every  trilateral  is  triangular  ?"  How 
is  it  possible  to  pronounce  that  to  be  a  simple  judgment  which  is  di- 
visible into  two,  and  especially  when  one  of  these  may  be  thought 
without  the  other,  when  one  may  be  known  and  the  other  unknown, 
when  one  may  be  false  and  the  other  true?  If  "All  triangles  are  all 
trilaterals  "  is  only  one  judgment,  what  is  "  All  triangles  are  trilateral  ? 
Is  it  half  a  judgment  ? 

In  Hamilton's  support  of  afa  he  says :  "  Ordinary  language  quanti- 
fies the  predicate  as  often  as  this  determination  becomes  of  the  small- 
est import  This  it  does  directly  by  adding  a//,  some,  or  their  equiv- 
alent predesignations  to  the  predicate;  or  it  accomplishes  the  same 
end  indirectly,  in  an  exceptive  or  limitative  form.  E.  g.,  Directly :  as, 
*  Peter,  James,  John,  etc.,  are  all  the  apostles.'  E.  g.,  Indirectly:  as, 
''God  alone  is  good,' i.  e.,  *  God  is  all  that  is  good;'  *  Virtue  is  the 
only  nobility,'  i.  e.,  *  Virtue  is  all  that  is  noble ;'  '  On  earth  there  is 
nothing  great  but  man,'  i.  e., i  Man  is  all  earthly  great.'  " e  Now  the 
doctrine  of  logicians  has  always  been,  as  stated  by  Scheibler :  Omnis 
exclusiva  resolvitur  in  duas  simplices,  alteram  affirmatam,  alteram 
negatam.  This  view  has  already  been  discussed  (i,  §  12).  If  it  be 
correct,  if  such  exceptive  and  exclusive  propositions  are  compound, 
then  it  appears  from  Hamilton's  own  statement  and  illustrations,  that 
afa  is  a  compound  proposition. 

6ioyzV,  p.  517. 


INNOVATIONS.  123 

It  may  be  conceded  that  this  form  afa  is  familiar  in  speech,  that 
it  is  natural,  if  you  please,  that  men  make  constant  use  of  it  in  reason- 
ing, that  such  reasonings  are  easily  reducible  to  syllogistic  forms  in 
which  one  or  both  premises  are  afa,  that  brevity  and  perspicuity  are 
promoted  by  its  use,  and  hence  that  it  should  be  included  in  every 
logical  analysis  of  the  forms  of  human  thought.  But  .Logic  in  this 
proposed  analysis  cannot  stop  short  of  simple  and  ultimate  forms. 
If  it  were  an  art  teaching  ns  how  to  reason  or  even  how  to  detect 
error  in.  reasoning,  then  there  might  be  occasion  for  an  elaboration 
and  symbolizing  of  compound  forms,  though  indeed  the  work  would 
be  endless.  But  as  it  is  on  the  higher  ground  of  a  science,  one  show- 
ing how  we  do  and  must  think,  it  is  out  of  character  to  present  com- 
pound forms  as  the  results  of  analysis.  Now  whatever  can  be  proved 
from  All  A  is  all  B,  can  be  proved  from  one  or  both  of  its  elements — 
All  A  is  B,  and  All  B  is  A.  Whatever  can  be  proved  from  Some  A 
is  all  B,  can  be  proved  from  its  elements — Some  A  is  B,  and  All  B 
is  A.  It  is  not  possible  that  there  should  be  a  single  instance  in 
which  a  conclusion,  provable  from  premises  with  quantified  predicates, 
could  not  be  proved  from  the  same  unqualified,  if  we  set  forth  all 
those  which  are  really  involved.  If  there  could  be  such  an  instance, 
the  doctrine  of  a  quantified  predicate  would  be  a  real  addition  to  the 
theory  of  thought ;  otherwise  not.7 

Consequently,  supported  by  the  authority  of  Mill,  De  Morgan,  Bain, 
and  others,  we  object  to  the  intrusion  of  the  compound  form  afa,  and 
its  train,  among  the  simple  forms,  and  reject  the  doctrine  of  "  The 
Thorough-going  Quantification  of  the  Predicate,"  taught  by  Ham- 
ilton. We  are  glad  to  escape  from  the  fearful  complications  into 
which  it  leads,  and  rest  in  the  comparative  simplicity  of  the  Aristo- 
telic  Logic;  and  we  honor  the  old  logicians  in  the  belief  that,  during 
the  two  thousand  years  of  their  acute  discussions,  these  forms  were 
surely  considered,  and  were  not  allowed  in  their  system  because  they 
did  not  belong  to  the  fold,  and  if  admitted  would  ravage  the  flock. 

§  6.  The  foregoing  argument  is  sufficient  to  refute  Hamilton's  doc- 
trine, and  exclude  his  forms  from  among  the  Aristotelic.  The  view 
taken  is  complete  as  against  him ;  but  it  does  not  completely  exhibit 
the  ultimate  character  of  afa  and  its  cognates.  Let  us  examine  their 
nature  yet  more  closely.  We  have  pronounced  them  compounds.  It 

7  See  Mill's  Examination  of  Hamilton's  Philosophy,  ch.  xxii. 


124  OF    JUDGMENTS. 

would  perhaps  be  more  accurate  to  say  that  each  results  from  the 
compounding  of  two  simple,  logical  judgments,  and  becomes  a  simple 
mathematical  judgment.  This  needs  some  explanation. 

Hamilton  speaks  continually  of  distributed  and  undistributed  predi- 
cates. The  old  Logic,  too,  uses  the  same  expressions,  but  only,  as 
we  have  said,  precursory  to  conversion,  which,  indeed,  is  already  accom- 
plished as  soon  as  the  quantification  is  thought  into  the  predicate.  We 
have  denied  that  the  predicate  of  a  purely  simple  logical  judgment  has, 
or  can  have,  any  quantification  whatever,  affirming  that  it  is  absolutely 
indefinite.  We  now  add,  that  a  quantitative  predesignation  thrust  in 
upon  a  predicate  by  the  compounding  of  two  simple  judgments  re- 
moves the  judgment  from  the  logical  or  qualitative  whole,  and  trans- 
fers it  to  the  quantitative  or  mathematical  whole.  Hence,  if  we  view 
the  judgment  in  reference  to  its  origin,  we  may  call  it  compound,  or 
compounded;  but  if  we  view  it  in  its  own  sense,  we  must  no  longer 
call  it  a  logical,  but  a  simple  mathematical  judgment  (i,  §  13). 

For,  consider  the  meaning  of  "all"  in  the  predicate.  It  is  not,  it 
cannot  be,  the  distributive,  divisive,  exemplar  "  all,"  but  is  always  the 
total,  indivisible,  cumular  "all,"  a  mathematical  whole.  E.g.,  "All 
men  are  bimana;"  this  is  the  distributive  "all,"  meaning  that  all, 
each,  and  every  man  is  in  the  class,  or  has  the  mark,  bimana.  But  let 
us  say  "All  men  arc  all  bimana;"  this  does  not  mean  "Every  man 
is  all  bimana,"  nor  "  All  men  are  every  bimana,"  nor  "  Every  man  is 
every  bimana,"  which  is  nonsense.  It  means  "All  men  (as  a  mathe- 
matical, total,  collective  whole)  are  all  bimana  "  (as  ditto).  Thus  "  all " 
in  the  predicate  is  never  distributive,  but  cumular,  and  enforces  the 
"  all "  of  the  subject  also  to  be  cumular.  So  also  the  total  predicate 
of  a  negative  is  a  mathematical,  not  a  distributed  total ;  and  "  some  " 
in  the  predicate  is  a  mathematical  part.  More  generally,  whenever 
the  quantity  of  the  predicate  is  designated,  both  terms  are  individ- 
uals, and  the  judgment  is  mathematical.  The  effect  of  thus  quantify- 
ing the  predicate  is  to  transmute  the  judgment  from  the  qualitative  to 
the  quantitative  whole,  in  which  it  is  simple.  This  shows  that  Ham- 
ilton's "  distributed  predicate  "  is  a  complete  misnomer,  and  the  fact 
is  fatal  to  his  doctrine.8 

8  To  avoid  future  misapprehension,  we  will  note  that,  though  denying  to  the 
Hamiltonian  forms  the  rank  and  important  position  assigned  to  them  in  Logic 
by  their  author,  we  may  have  occasion  to  use  them,  for  the  sake  of  brevity,  in  syl- 
logizing. Also  we  shall  be  free  to  use  his  nomenclature  and  notation,  which  we 
esteem  a  valuable  contribution  to  the  appliances  of  technical  logic. 


PART  FOURTH.— OF  REASONINGS. 


I.  THE   SYLLOGISM. 

§  1.  The  logical  and  natural  treatment  of  a  subject  requires  that  its 
definition  be  first  ascertained,  which  fixes  its  relations  to  superior 
notions;  then  that  its  subdivisions  be  ascertained,  which  fixes  its 
kinds.  First  its  connotation  is  settled,  then  its  denotation.  Thus,  in 
general,  let  us  proceed  with  the  subject  now  before  us. 

We  have  already  defined  thought  in  a  general  sense  to  be  the  bring- 
ing one  notion  in  or  under  another.  This  duplex  definition  obviously 
refers  to  the  two  quantities  of  thought,  the  intension  and  the  exten- 
sion. The  distinction  between  these  is  thorough-going;  we  met  it 
at  the  outset  in  concepts ;  we  found  that  cjiven  judgments  may  be 
construed  in  either  quantity ;  and  we  shall  find  the  same  to  be  true  of 
reasonings.  As  every  notion  may  be  viewed  either  as  a  complement 
of  marks,  or  as  a  kind  of  a  thing,  so  every  reasoning  may  be  viewed 
either  as  a  bringing-in  marks  into  a  notion,  or  as  a  bringing  the  no- 
tion under  a  genus.  But  let  it  be  remembered  that  intension  and  ex- 
tension always  coexist,  and  that  thought  is  readily  transmuted  from 
the  one  into  the  other. 

"We  have  also  said  that  thought  is  either  by  conceiving  or  by  judg- 
ing. Now  let  it  be  again  observed  that  conception  and  judgment  are 
not  two  kinds  or  species  of  thought,  but  one  and  the  same  thing  in  a 
different  form,  or  viewed  under  different  aspects  or  phases.  Every 
concept  is  an  implicit  judgment,  and  every  judgment  is  an  explicit 
concept.  Consequently  the  definition  given  above  of  thought  is  equal- 
ly the  definition  of  conceiving  and  of  judging. 

There  are,  however,  two  kinds  of  conception,  the  immediate  or  di- 
rect, and  the  mediate  or  indirect.  The  first  has  been  treated  in  Part 
Second.  It  is  the  direct  comparison  of  two  notions  by  which  they 
are  immediately  conjoined,  or  disjoined.  The  second  occurs  when  we 
are  through  ignorance  unable  to  make  a  direct  comparison,  and  re- 


126  OF    REASONINGS. 

sort  to  a  medium,  i.  e.,  some  third  notion,  which  being  directly  com- 
pared with  each  of  the  two  former  enables  us  to  see  their  agreement 
or  disagreement,  and  consequently  to  conjoin  or  disjoin  them.  This 
is  mediate  conception.  Immediate  conception  has  received  no  specific 
name,  and  is  always  understood  when  the  unqualified  word  is  used. 
Mediate  conception  is  called  reasoning.  This,  then,  is  the  logical  def- 
inition :  Reasoning  is  mediate  conception. 

Let  us  exemplify  reasoning  in  this  view.  I  have  the  notion  man 
and  the  notion  free-willed.  On  comparing  these,  I  am  unable  to  de- 
cide whether  or  not  this  mark  belongs  to  that  concept.  By  the  prin- 
ciple of  the  Law  of  Excluded  Middle  I  am  constrained  to  believe 
that  it  either  does  or  does  not ;  but  which,  I  cannot  immediately  de- 
termine. So  I  seek  a  medium  of  comparison.  I  take  the  notion  re- 
sponsible, and  I  see  directly  that  the  notion  man  involves  this  notion 
responsible,  likewise  that  the  notion  responsible  involves  the  notion 
free  ;  and  thus  I  see  that  the  notion  man  involves  as  one  of  its  marks 
the  notion  free.  This  is  the  intensive  view.  If  1  proceed  rather  in 
the  extensive  quantity,  the  matter  would  be  expressed  thus :  I  am  un- 
able directly  to  decide  whether  or  not  man  is  a  kind  of  free-agent. 
But  I  know  that  the  class  free-ag cnts  contains  under  it  the  species  re- 
sponsible agents,  and  that  this  contains  under  it  man  ;  and  so  I  am 
able  now  to  think  that  the  class  free-agents  contains  under  it  man  as 
one  of  its  kinds. 

In  exact  accordance  with  this,  we  now  observe  that  there  are  two 
kinds  of  judgments,  the  immediate  or  direct,  and  the  mediate  or  indi- 
rect. Immediate  judgment  has  been  considered  in  Part  Third.  It 
also  is  the  direct  comparison  of  two  notions,  but  issues  in  the  explicit 
declaration  that  they  are  conjoined  or  disjoined.  Mediate  judgment  oc- 
curs when,  not  being  able  directly  to  judge  this  agreement  or  disagree- 
ment, we  seek  a  third  notion  as  a  medium  of  comparison,  and  explicitly 
state  that  each  of  the  other  notions  does  or  does  not  agree  with  this 
third;  and  thus  we  are  enabled  to  conclude  explicitly  whether  they  do 
or  do  not  agree  with  each  other.  This  is  mediate  judgment.  Immedi- 
ate judgment  has  received  no  specific  name,  and  is  always  understood 
when  the  unqualified  word  is  used.  Mediate  judgment  is  called  reason- 
ing. The  logical  definition, then,  is:  Reasoning  is  mediate  judgment. 

It  is  quite  evident  that  there  is  no  essential  difference  between  me- 
diate conception  and  mediate  judgment ;  the  difference  is  merely  for- 
mal, and  is  usually  neglected.  Also  it  is  evident  that  a  mediate  judg- 
ment when  expressed  in  words  will  exhibit  three  propositions.  Let 


THE    SYLLOGISM.  127 

us  not  be  misled  by  this  appearance  to  suppose  that  a  reasoning  is 
three  judgments.  Aristotle  insists,  and  all  logicians  agree,  that  the 
reasoning,  which  is  the  act  of  mediate  comparison,  and  which  from 
two  given  judgments  having  a  common  part  concludes  a  third,  is  but 
a  single  act  of  mind,  a  single  thought,  only  one  judgment. 

We  will  now  exemplify  reasoning  viewed  as  a  mediate  judgment. 
I  do  not  know  whether  to  affirm  or  deny  that  man  is  free.  So  having 
found  a  medium  of  comparison,  I  express  myself  thus, — 

Man  is  responsible ; 
One  responsible  is  free ; 
therefore,  Man  is  free. 

This  is  evidently  thinking  in  the  quantity  of  intension.  Treating  the 
same  matter  extensively,  I  would  say, — 

Every  responsible-agent  is  a  free-agent; 
Every  man  is  a  responsible-agent ; 
therefore,  Every  man  is  a  free-agent. 

In  order  expressly  to  distinguish  the  intensive  from  the  extensive 
quantity,  we  interpret  the  copula  of  the  former  as  "  comprehends"  and 
that  of  the  latter  as  "  is  contained  under"  The  above  more  explicitly 
stated  would  then  be  as  follows, — 

{The  notion  man  comprehends  the  notion  responsible; 
The  notion  responsible  comprehends  the  notion  free ; 
.*.  The  notion  man  comprehends  the  notion  free. 

f      The  notion  responsible-agent  is  contained  under  free-agent ; 
Extensively  •<       The  notion  man  is  contained  -under  the  notion  responsible-agent ; 
(  .'.  The  notion  man  is  contained  under  the  notion  free-agent. 

Since  conception  and  judgment  are  merely  different  forms  of 
thought,  it  is  perfectly  competent  to  unite  the  two  synonymous  defi- 
nitions of  reasoning  given  above  into  one,  and  define  thus:  Reason- 
ing is  mediate  thought.  Again,  as  all  thought  is  comparison :  Rea- 
soning is  mediate  comparison.  Again,  we  found  in  Part  Third  that 
to  infer  is  to  derive  one  judgment  from  one  or  more  others,  and  that 
immediate  inference  or  illation  does  this  directly,  from  a  single  ante- 
cedent. We  now  find  that  mediate  inference  docs  this  indirectly, 
from  two  antecedent  judgments  having  a  common  part ;  hence,  we 
may  define  once  more :  Reasoning  is  mediate  inference  or  illation. 

A  mediate  judgment,  when  presented  as  in  the  examples  given 
above,  is  called  a  Syllogism.  What  is  subjectively  a  Reasoning,  is  ob- 
jectively a  Syllogism.  Hence  we  define :  A  Syllogism  is  a  reasoning 
fully  and  regularly  expressed  in  language.  What  is  meant  by  "  regu- 


128  OF    REASONINGS. 

larly  "  will  hereafter  more  clearly  appear.  Another  definition  is :  A 
Syllogism  is  an  inference  by  which  one  proposition  is  derived  from 
two  others  conjointly,  the  one  being  virtually  contained  in  the  others. 
Aristotle  opens  his  Prior  Analytics  with  this  definition :  "  A  Syllo- 
gism is  an  enunciation  (Aoyoe,  oratio)  in  which,  from  something  laid 
down  and  admitted,  something  distinct  from  what  we  have  laid  down, 
follows  of  necessity." 

Let  us  consider  at  once  the  import  of  this  last  phrase,  "  follows  of 
necessity."  The  essence  of  a  syllogism  consists,  not  in  the  truth  of 
the  propositions  laid  down,  nor  in  the  truth  of  that  which  is  inferred, 
but  in  the  production  of  a  new  and  distinct  judgment,  the  truth  of 
which  cannot  be  denied  without  impugning  those  we  have  already  ac- 
cepted for  true.  In  other  words,  the  essence  of  the  syllogism,  and  all 
that  is  actually  declared  by  it,  is  the  necessary  consequence  of  the 
conclusion  from  the  premises.  This  necessity  flows  from  the  neces- 
sary character  of  the  primary  laws  of  thought,  to  which  the  syllogism 
conforms  and  by  which  alone  it  is  ultimately  governed.  It  is  fre- 
quently expressed  in  the  conclusion  by  the  addition  of  "must."  For 

example, — 

Since  all  metals  are  fusible, 
And  gold  is  a  metal, 
Gold  must  be  fusible. 

The  common  distinction,  then,  between  demonstrative  and  moral  or 
probable  reasoning,  lies  wholly  in  the  matter,  not  at  all  in  the  form. 
The  form,  or  rather  the  process,  by  which  we  infer,  is  in  all  cases  the 
same,  and  is  in  all  cases,  if  correct,  equally  demonstrative,  i.  e.,  apodic- 
tic,  necessary. 

The  affirmation  of  necessary  sequence  being  the  essence,  it  follows 
that  the  syllogism  is  really  only  one  judgment,  a  single  indivisible  act 
of  thought.  Though  apparently  complex,  though  in  a  certain  sense 
including  three  judgments,  it  does  not  affirm  either  of  them  taken 
separately,  but  only  the  necessary  dependence  of  one  on  the  others. 
It  is  a  judgment  concerning  judgments,  one  affirming  the  relation  of 
sequence,  and  may  easily  be  expressed  in  a  single  proposition ; 
e.  g.,  That  gold  is  fusible  is  an  inference  from  the  judgments  that  it 
is  one  of  the  metals,  and  that  they  are  all  fusible. 

Another  consequence  of  this  doctrine  is  that  Logic  does  not  con- 
cern itself  with  the  truth  or  falsity  of  the  several  propositions.  One 
or  all  may  be  false,  but,  having  granted  the  antecedents,  the  consequent 
must  also  be  allowed,  if  the  reasoning  is  sound,  the  syllogism  regular. 


THE    SYLLOGISM. 

We  may,  however,  note  that  the  antecedents  being  true,  the  consequent 
is  necessarily  true.  Also,  what  measure  of  doubt  belongs  to  the  ante- 
cedents, just  that  measure  of  doubt,  no  more,  no  less,  belongs  to  the 
consequent.  But  should  the  antecedents  be  found  false,  it  does  not 
follow  that  the  consequent  is  false ;  it  is  simply  unproven,  and  may 
be  established  as  true  upon  some  other  antecedents.  For  example, — 

The  natives  of  Italy  were  Greeks ; 
The  Athenians  were  natives  of  Italy ; 
.'.  The  Athenians  were  Greeks. 

Grant  these  antecedents,  and  the  consequent  must  be  admitted,  for  it 
follows  of  necessity.1  But  both  antecedents  are  obviously  false,  yet  the 
consequent  is  not  false,  for  we  can  prove  it  from  other  antecedents. 

Before  entering  upon  another  section,  two  additional  remarks  may  be 
appended.  A  syllogism  is  an  expression  of  one  of  the  units  of  which 
the  most  elaborate  argument  is  only  the  sum.  The  longest  chain  or 
most  complex  net-work  of  reasoning  may  be  stated  in  syllogisms 
linked  together.  The  links  are  quite  similar.  When  we  thoroughly 
understand  one,  in  its  characters  and  kinds,  we  understand  all.  It  is 
true  that  an  argumentation  does  not  usually  present  the  form  of  syl- 
logisms ;  its  steps  are  much  abbreviated  by  elisions  and  variations  from 
form  ;  but  however  elaborate  it  may  be,  still  it  can  be  resolved  into  its 
elementary  syllogisms,  and  these  stated  in  regular  form  and  consecu- 
tion. Moreover,  much  of  our  common-place  thinking  and  conversa- 
tion, even  many  of  our  lightest  witticisms,  if  closely  analyzed  and 
fully  stated,  will  be  found  to  resolve  into  syllogisms. 

The  other  remark  is  but  a  repetition  of  one  previously  made.  In 
the  study  of  reasoning  we,  of  course,  are  not  advancing  beyond  com- 
plete system.  The  function  of  reasoning  or  mediate  judgment  is 
solely  to  make  our  concepts  more  clear  and  distinct,  to  ascertain  their 
true  relations  to  each  other,  and  thus  to  fix  their  places  in  the  hie- 
rarchies of  our  thoughts,  which  thereby  approximate  more  and  more 
to  complete  systems,  the  perfection  of  knowledge. 

1  See  Anal.  Priora,  bk.  ii,  ch.  ii;  and, per  contra,  Esser,  in  Hamilton's  Logic^  p.  322. 
It  may  be  well  to  say  here  that  the  doctrine  of  the  Syllogism,  as  treated  by  Aristotle 
in  the  Prior  Analytics,  should  be  carefully  read  by  every  student  of  Logic.  The 
best  text  of  the  Organon  is  probably  that  of  Theo.  Waitz,  accompanied  by  his  val- 
uable Latin  commentary ;  but  it  is  to  be  regretted  that  the  isagogue  of  Porphyry  ' 
has  not,  at  least  in  the  edition  I  am  using  (Leipsic,  1844),  been  included.  The 
translation  and  commentary  of  St.  Hilaire  is  classical,  and  must  not  be  neglected. 
For  English  readers  Owen's  translation  and  notes  (Bohn's  ed.),  and  Poste's  text, 
translation,  and  notes  on  De  Soph.  (Macmillan,  1866),  arc  excellent. 


130  OF    REASONINGS. 

§  2.  The  next  step  in  the  treatment  of  the  syllogism,  like  that  in 
our  treatment  of  the  proposition,  is  to  view  it  as  a  mathematical  or 
quantitative  whole,  and  sever  it  by  partition.  The  parts  thus  obtained 
by  dissection  are  to  be  examined  and  named,  and  their  relations  indi- 
cated. We  will  then  proceed  to  consider  the  kinds  of  syllogism. 

The  syllogism,  as  has  been  anticipated,  consists  of  three  propo- 
sitions, two  of  which  are  called  the  antecedents,  and  the  third,  the 
consequent.  The  antecedents  are  also  called  the  premises,  and  the 
consequent,  the  conclusion.  To  conclude  (con-cludere)  is  to  shut  up 
together  in  the  last  proposition  notions  which  stood  apart  in  the  first 
two.  So  also  the  word  "  syllogism "  (aw-Xiytiv)  signifies  a  collect- 
ing together ;  as  when  Aristotle  describes  a  conclusion  as  "  a  perfect 
syllogism  of  the  extremes."  The  following  is  an  example  in  the 
quantity  of  extension, — 

All  Men  are  Persons ;     =M:  •—  P  —  Major  Premise ; 
All  Slaves  are  Men ;        =  S:  —  M  =  Minor  Premise ; 
.*.  All  Slaves  are  Persons ;  =  S:  »—  P  =  Conclusion. 

There  are  here  only  three  terms  or  notions,  "  Slaves,  Men,  Persons." 
It  is  evident  that  these  stand  to  each  other  in  the  relation  of  whole 
and  part,  Slaves  being  contained  under  Men,  and  Men  being  contained 
under  Persons.  Persons,  then,  is  the  term  of  widest  extent  (as  in  the 
symbols) ;  Slaves,  the  term  of  least  extent ;  and  Men  of  intermediate 
extent.  This  M,  which  is  called  the  Middle  Term,  is  found  in  each 
of  the  premises,  but  not  in  the  conclusion.  The  other  two  terms, 
which  together  are  called  the  Extremes,  are  both  found  in  the  conclu- 
sion ;  separately  they  are  called  the  Major  Term  and  the  Minor  Term. 
Hence  we  may  define  as  follows, — 

The  Middle  Term  (M)  is  the  one  with  which  each  of  the  extremes 

is  compared  in  the  premises.     It  is  also  called  the  Argument. 
The  Major  Term  (P)  is  the  term  of  greatest  quantity,  or  the  greatest 

whole.    It  is  always  (in  extension)  the  Predicate  of  the  conclusion. 
The  Minor  Term  (S)  is  the  term  of  least  quantity,  or  the  least 

whole.     It  is  always  (in  extension)  the  Subject  of  the  conclusion. 
The  Major  Premise  is  the  premise  containing  the  Major  Term.     It 

is  usually  placed  first. 
The  Minor  Premise  is  the  premise  containing  the  Minor  Term.     It 

is  usually  placed  second. 


THE    SYLLOGISM.  131 

Examples  in  the  quantity  of  intension  will  now  be  given.  We 
transmute  the  one  above  into  this  quantity,  and  add  one  other, — 

All  Slaves  are  human ;  Silver  is  Metallic ;  =  S:  — » M  \ 

All  the  human  are  Personal ;  Metal  is  Positive ;  =  M:  —  P  >•  =  S:  —  M:  — i  P 
/.  All  Slaves  are  Personal.  /.  Silver  is  Positive.  =  S:  —  P  ) 

The  expression,  for  the  sake  of  form  and  brevity,  is  permitted  to  be 
somewhat  awkward.  By  "  Positive  "  is  meant  electro -positive.  In 
the  graphic  notation'2  on  the  right,  the  long  pointed  dash  below  is  the 
copula  of  the  extremes  in  the  conclusion.  This  condensed  form  is 
read  exactly  like  that  standing  just  before  it.  The  extensive  syllo- 
gism can  of  course  be  expressed  in  a  similar  way,  only  the  copulas 
are  inverted.  When  we  read  in  the  direction  that  the  copula  points, 
i.  e.,  extensively,  it  should  be  read  "  is  contained  under  ;"  when  we  read 
in  the  direction  opposite  to  that  the  copula  points,  i.  e.,  intensively, 
it  should  be  read  ** comprehends" 

In  changing  the  extensive  syllogism  into  the  intensive,  the  middle 
term  continues  intermediate,  but  the  relative  quantity  of  the  extremes 
is  inverted;  the  greatest  part  in  extension  (P)  becomes  the  least  part 
in  intension,  and  vice  versa.  This  is  in  accord  with  the  law  that  ex- 
tension and  intension  are  in  inverse  ratio.  In  the  example  "  Silver 
comprehends  Metallic,  and  this  comprehends  Positive,"  S  is  obviously 
the  greatest  whole,  and  P  the  least.  Hence,  in  intension  the  major 
term  is  the  Subject  of  the  conclusion,  and  the  minor  term  is  the 
Predicate  of  the  conclusion.  And  hence,  since  it  is  usual  to  place  the 
major  premise  first,  the  order  of  the  premises  is  transposed.  We 
have,  then,  for  changing  a  syllogism  of  either  quantity  into  the 
other,  the  following  RULE  :  Transpose  the  premises,  and  invert  in 
thought  the  meaning  of  the  copula;  i.  e.,  instead  of  "comprehends" 
think " is  contained  under"  and  vice  versa.  For  example. — 


All  Metals  are  Positive  elements ; 
(  .*.  Silver  Is  a  Positive  element. 


5) 
In  Extension     -J      Silver  is  a  Metal ;  P  —  :M  —  :i 


Aristotle's  definition  of  the  terms  of  a  syllogism  is  so  general  that 
it  will  apply  to  either  quantity,  which  renders  it  probable  that,  unlike 
his  followers,  he  recognized  both.  "  I  call,"  he  says  in  the  first  part 
of  the  Prior  Analytics,3  "  the  middle  term  that  which  is  both  itself  in 
another  and  another  in  it ;  and  which  by  its  position  lies  in  the  mid- 

8  See  Part  3d,  iii,  §  3.  a  Ch.  iv. 


132  OF    REASONINGS. 

die.     The  extremes  I  call  both  that  which  is  in  another,  and  that  in 
which  another  is.     I  define  the  major  extreme  as  that  in  which  the 
middle  is ;  the  minor  extreme,  as  that  which  is  under  the  middle." 4 
Aristotle's  method  of  stating  the  syllogism  differs  from  ours.     It 

is  thus : 

P  inheres  in,  or  is  predicated  of,  all  M ; 

M  inheres  in,  or  is  predicated  of,  all  S ; 

.'.  P  inheres  in,  or  is  predicated  of,  all  S. 

It  will  be  observed  that  here  the  major  premise  (in  extension)  stands 
first.  This  brings  the  middle  term,  as  he  says  above,  into  the  mid- 
dle position.  Soon  after  his  day  logicians,  preferring  to  state  the 
propositions  in  their  natural  form  with  the  subject  first,  transposed 
the  premises,  in  order  to  keep  the  middle  term  in  the  middle  position. 

We  have,  then,  the — 

(       All  S  is  M ; 

Ancient  order  <       All  M  is  P ; 

(  /.  All  S  is  P. 

This  order  was  observed  until  the  time  of  Bocthius,  who  thought  it 
more  important  to  place  the  major  premise  first,  returning  in  this  re- 
spect to  Aristotle,  and  these  high  authorities  determined  subsequent 
usage.  Consequently  in  our  method  of  stating  the  syllogism  in  ex- 
tension, the  only  quantity  recognized  from  the  time  of  Aristotle  until 
recently,  the  middle  term  does  not  have  middle  place. 

There  seems,  however,  no  valid  reason  why  the  major  premise 
should  have  precedence.  It  is  said  that  it  is  more  natural  to  begin 
our  statement  with  the  greatest  whole.  It  may  be  so,  but  in  the 
actual,  practical  expression  of  a  reasoning  we  often  find  the  order  of 
all  the  propositions  completely  inverted,  the  conclusion  being  placed 
first  as  a  qucesitum,  or  problem,  or  thesis,  and  the  premises  following 
in  reversed  order ;  as,  "  Silver  is  a  positive  element ;  for  it  is  a  metal, 
and  all  metals  are  positive  elements."  Is  not  this  quite  a  natural 
order  of  statement  ?  If  so,  then  unquestionably,  unless  a  more  satis- 

4  Anal  Pri.  i,  iv.  'O  /t£<roc.  nal  al  aKpat.  The  middle  term  is  the  bridge  be- 
tween them.  Properly,  when  we  inquire  after  the  meaning  of  a  thing  we  are  seek- 
ing the  mean  or  middle  term  or  notion.  E.  g.,  "  What  mean  ye  by  this  service  ?" — 
Ex.  xii,  26.  Meanness,  as  applied  to  our  using  means,  has  acquired  a  bad  sense. 

Can  you  imagine  I  so  mean  could  prove, 

To  save  my  life  by  changing  of  my  love  ? — Dryden. 

The  monkey  using  the  cat's  paw,  is  a  proverbial  specimen.  Barring  the  had  sense, 
the  middle  term  is  the  logical  cat's  paw. 


THE    SYLLOGISM.  133 

factory  reason  can  be  adduced,  we  are  justified  in  viewing  the  ap- 
proved order  of  the  premises  as  arbitrary,  merely  a  matter  of  conven- 
tion and  custom.5 

Kant  takes  a  somewhat  different  view  of  reasoning  and  the  syllo- 
gism. Reasoning  is  bringing  a  case  under  a  general  rule,  and  so  de- 
termining it.  In  the  syllogism  the  major  premise  is  a  rule,  the  asser- 
tion of  a  general  condition,  the  Sumption  (Obersatz).  The  minor 
premise  is  the  cognition  that  the  condition  of  the  rule,  somewhere  or 
other,  takes  place ;  or,  is  that  which  brings  a  case  under  the  condi- 
tion of  the  rule,  the  Subsumption  ( Vntersatz).  The  nexus  of  what 
is  subsumed  under  the  condition,  with  the  assertion  of  the  rule,  is 
the  Conclusion  (Schlusssatz).  Hence  a  syllogism  is  the  cognition 
that  a  certain  proposition  is  necessary,  through  the  subsumption 
of  its  condition  under  a  given  general  rule.  Hereby  we  understand 
the  conclusion  a  priori,  not  as  manifested  in  things  individual,  but  as 
universally  maintained,  and  as  necessary  under  a  certain  condition. 
And  this,  that  all  stands  under  the  universal,  and  is  determinable  in 
universal  laws,  is  the  principle  itself  of  rationality  or  of  necessity.8 

§  3.  In  proceeding  now  to  the  consideration  of  kinds,  we  notice, 
first,  the  common  division  of  reasonings  into  deductive  and  inductive. 
Deduction  consists  in  drawing  a  less  general  or  a  particular  truth  from 
a  general  truth  antecedently  known.  Induction  consists  in  rising  from 
particular  facts  to  the  determination  of  a  general  rule  or  law.  It  is 
evident,  then,  that  the  account  which  has  just  been  given  of  reason- 
ing and  the  syllogism  relates  exclusively  to  deductive  thought.  Many 
writers  on  Logic,  accepting  induction  as  a  kind  of  reasoning  opposed 
to  deduction,  attempt  to  subject  the  inductive  process  to  syllogistic 
forms  and  laws.  The  results  are  not  profitable  nor  commendable. 

6  Likewise  in  the  following  the  order  of  the  propositions  of  the  involved  syllogism 
is  completely  reversed : 

"  Qui  melior  servo,  qui  liberior  sit  avarus, 
In  triviis  fixum  cum  se  demittit  ob  assem, 
Non  video ;  nam  qui  cupiet  metuet  quoque ;  porro, 
Qui  metuens  vivet  liber  mihi  non  erit  unquam." — Hor.  Epist.  i,  16. 

The  argument  re-ordered  may  be  stated  thus : 

Whoever  is  fearful  is  not  free Sumption. 

The  miser  is  fearful Subsumption. 

.'.  No  miser  is  free Conclusion. 

6  See  Logik,  §§  56-58. 


134  OF   REASONINGS. 

An  examination  of  such  views  must  be  deferred.  They  are  men- 
tioned here  only  to  say  that  it  is  at  least  very  questionable  whether 
the  inductive  process  can  properly  be  viewed  as  a  species  of  reason- 
ing at  all,  certainly  not  under  the  definitions  of  reasoning  we  have 
given.  Without  present  discussion,  it  will  be  understood  that  by  rea- 
soning we  mean  the  deductive  process,  and  hold  that  the  syllogism 
and  its  laws  pertain  exclusively  to  it. 

Since  the  sumption  of  a  syllogism  is  a  general  rule,  or  since  the 
major  premise  contains  notions  of  wide,  often  of  absolute,  generality, 
the  question  may  have  already  arisen  in  the  mind  of  the  reader, 
Whence  are  they  obtained  ?  To  say  they  are  the  conclusions  of  prior 
and  wider  reasonings  may  in  most  cases  be  true,  but  is  an  insufficient 
answer,  for  the  same  question  recurs  as  to  these.  What,  then,  is  the 
ultimate  source  of  these  generalities?  We  answer,  it  is  either  intui- 
tion or  induction.  By  the  former  we  know,  for  example,  that  "  Every 
change  is  caused;"  by  the  latter,  that  "The  volume  of  gas  is  in  the 
inverse  ratio  of  the  pressure."  Sciences  whose  deductions  are  wholly 
from  intuitive  truths  are  called  a  priori,  or  pure,  or  demonstrative 
sciences;  those  whose  deductions  are  from  both  intuitive  truths  and 
inductions  are  called  a  posteriori,  or  empirical,  or  inductive  sciences. 

The  next  division  of  syllogisms  to  be  noticed  is  into  intensive  and 
extensive.  This  has  already  been  sufficiently  examined  in  the  preced- 
ing sections,  introduced  there  because  needful  in  order  to  general  def- 
inition, and  to  a  complete  view  of  the  relations  of  the  dissected  parts. 
We  are  now  prepared  to  make  an  estimate,  briefly  and  once  for  all,  of 
the  importance  of  this  distinction.  Hamilton,  to  whom  we  are  in- 
debted for  introducing  it  into  the  logical  literature  of  our  language, 
strenuously  insists  at  great  length  that  it  is  all -important,  the  two 
quantities  of  thought  yielding  two  distinct  kinds  of  reasoning.  Rea- 
soning in  intension,  he  says,  is  the  simpler  and  more  natural  form  of 
reasoning ;  and  in  introducing  it  he  claims  to  have  "  relieved  a  radical 
defect  and  vital  inconsistency  in  the  present  logical  system." 

We  cannot  refuse  to  the  modes  thus  distinguished  the  title  of 
kinds ;  but  how  much  in  this  case  is  it  worth  ?  The  external  dif- 
ference consists  wholly  in  transposed  premises.  But  the  order  of  the 
premises  being  merely  conventional,  any  distinction  founded  thereon 
is  entirely  arbitrary  and  artificial,  not  real  and  natural,  and  hence  goes 
for  nothing.  It  is  merely  a  convenient  way  by  which  we  agree  to  in- 
dicate which  quantity  is  intended.  The  other  difference  named  in 
the  rule  is  in  the  inverted  meaning  of  the  copula.  This  is  not  an  ex- 


THE    SYLLOGISM.  135 

ternal  difference.  In  ordinary  language  the  copula  is  wholly  indiffer- 
ent and  ambiguous,  and  we  can  indicate  its  special  meaning  only  by 
unusual  substitutions.  The  slight  grammatical  difference  which  some- 
times, but  not  always,  occurs  between  substantive  and  adjective  noun 
forms  in  the  predicate  cannot  be  regarded  as  a  logical  difference. 

The  difference,  then,  lies  entirely  in  thought,  and  consists  of  that 
between  the  wholes  of  extension  and  intension,  and  of  the  reversed  re- 
lation of  parts  and  whole.  That  this  constitutes  a  difference  in  kind 
we  have  granted,  one  which  must  be  observed  in  an  exposition  of 
mental  modes,  and,  we  may  admit,  in  a  theory  of  thought,  but  it  is  of 
very  small  logical  or  practical  consequence.  For  both  modes  are 
mediate  inferences  and  through  the  same  medium ;  both  reach  the 
same  conclusion  ;  the  formal  expression  of  both  is  the  same ;  the  su- 
preme canon  is  in  principle  the  same,  requiring  only  verbal  changes 
when  expressly  adapted  to  one  or  the  other  quantity;  the  general 
rules  of  the  syllogism  are  the  same  for  both,  not  requiring  even  a  ver- 
bal change ;  the  special  rules  are  the  same,  requiring  only  a  slight  ver- 
bal change — the  interchange  of  the  words  major  and  minor ;  hence 
no  modification  of  the  old  logical  doctrine  is  called  for  by  the  intro- 
duction of  the  intensive  syllogism. 

Moreover,  when  we  consider  that,  without  the  slightest  objective 
difference,  one  of  these  modes  subjectively,  and  with  the  greatest  facil- 
ity, changes  to  the  other,  and  that  without  further  consequence,  we 
ask,  What  is  the  worth  of  the  difference  between  two  things  so  com- 
pletely and  readily  transmutable  ?  Again,  it  is  highly  probable  that 
the  two  quantities  always  actually  coexist  in  thought  as  psychological 
correlatives,  one  being  usually  more  obscure  than  the  other.  If  so, 
their  convertibility  would  rather  indicate  identity,  being  inconsistent 
with  the  opposition  which  belongs  to  kinds.  And,  again,  we  re- 
mark that  Kant's  admirable  and  philosophic  view  of  reasoning  and 
the  syllogism  does  not  distinguish  the  quantities.  Finally,  we  often 
use  both  quantities  successively  in  the  same  reasoning.  For  example, — 

All  of  the  metals  are  positive Intensive. 

Silver  is  one  of  the  metals Extensive. 

.'.  Silver  is  positive .Intensive. 

Can  this  be  fairly  objected  to  ?  Hamilton  would  denounce  it  as  a 
hybrid ;  a  senseless  gymnastic,  hopping  from  one  quantity  into  an- 
other, and  back  again ;  possible,  but  stupid.7  I  cannot  admit  this, 

1  See  Lojic,  p.  303. 


136  OF    REASONINGS. 

and  believe  that  only  he  who  is  riding  a  hobby  would  find  it 
faulty. 

From  these  considerations  we  may  justly  conclude  that  the  distinc- 
tion between  extensive  and  intensive  syllogisms  is  of  very  small,  if  of 
any,  logical  moment,  and  certainly  very  far  from  deserving  the  empha- 
sis given  to  it  by  Hamilton,  and  repeated  with  passive  sequacity  by  so 
many  subsequent  writers.  We  shall  keep  it  in  view  only  for  the  sake 
of  more  complete  theory,  and  in  illustrations  use  indifferently  either 
quantity. 

The  following  divisions  of  the  syllogism  are  determined  simply  by 
the  kind  of  its  propositions.  The  general  division  is  into — 

The  Categorical  and  the  Conditional  syllogism.  We  shall  for 
some  time  continue  to  treat  of  the  former  exclusively.  The  consider- 
ation of  the  latter  is  postponed  to  a  subsequent  Topic. 

Categorical  syllogisms  may  be  variously  subdivided  into — 

1.  The  Simple  and  the  Compound.    The  latter  are  deferred  to  a  sub- 
sequent Topic.    The  simple  will  occupy  us  exclusively  for  the  present. 

2.  The  Total  and  the  Partial,  or  the  Universal  and  the  Particular. 
When  any  one  proposition  is  particular,  the  syllogism  is  particular, 
having  a  particular  conclusion.     When  all  three  propositions  are  uni- 
versal, the  syllogism  is  universal.     The  quantity  of  the  proposition 
determines  this  kind. 

3.  The  Positive  and  the  Negative.     When  one  premise  is  negative, 
the  syllogism  is  negative,  yielding  a  negative  conclusion.     The  quality 
of  one  premise  determines  this  kind.     The  two  latter  kinds,  depend- 
ing on  quantity  and  quality,  call  for  no  further  remark  at  present. 
They  may,  however,  be  here  jointly  illustrated  by  an  example  which 
has  one  premise  particular,  and  one  negative,  yielding  a  conclusion 
which  is  both. 

No  murmurs  are  prayers (E)       ^~^  Prayers. 

Some  sighs  are  murmurs (I) 


/.  Some  sighs  are  not  prayers...  .(0)  v   ~  J  ~"'S 

Finally,  categorical  syllogisms  are  divided,  according  to  the  relative 
position  of  the  middle  term,  into  four  Figures.  These  will  be  con- 
sidered under  the  Topic  next  following.  All  examples  thus  far  given 
are  in  the  first  figure. 

Under  the  present  Topic  it  remains  to  consider  the  Canon,  and  the 
General  Rules  of  the  categorical  syllogism. 


THE    SYLLOGISM.  137 

§  4.  The  judgment  whereof  the  syllogism  essentially  consists,  the 
judgment  that  the  antecedents  necessitate  the  consequent,  is  deter- 
mined by  the  three  primary  laws  of  thought.  Since  these,  however, 
because  of  their  wide  generality,  are  not  readily  applicable,  logicians 
have  sought  to  express  in  a  single  special  CANON  the  principle  of  syl- 
logism, a  Canon  that  is  only  a  special  statement  of  the  three  primary 
laws  as  governing  the  syllogism,  and  which  may  be  used  as  an  easy 
and  direct  test  of  its  validity.  The  results  of  these  attempts  are  not 
very  satisfactory,  the  several  forms  of  the  Canon  being  each  inade- 
quate ;  but  they  are  nevertheless  useful.  We  will  here  state  some  of 
the  most  noteworthy  : 

1.  "Part  of  a  part  is  part  of  the  whole."     Remembering  that  marks 
are  spoken  of  as  parts  of  a  concept,  and  species  as  parts  of  a  genus, 
this  axiom  is  obviously  applicable  to  both  quantities  of  thought,  and 
to  both  wholes,  the  logical  and  the  mathematical.    Its  generality,  brev- 
ity, and  simplicity  render  it  perhaps  the  most  useful  form.     It  is,  how- 
ever, inadequate,  being  applicable  only  to  affirmative  syllogisms.     A 
modified  form,  applicable  only  to  the  logical  whole,  is :  "  What  is 
said  distributively  of  a  whole  may  be  said  of  a  part."     If  the  reader 
will  apply  these  forms  to  either  of  the  foregoing  affirmative  syllogisms, 
the  meaning  will  be  sufficiently  obvious ;  and  it  will  also  become  evi- 
dent that  the  Canon  is  only  the  essential  judgment  of  the  syllogism 
generalized  in  second  intentions. 

2.  "  Contentum  contenti  est contentum  continentis" — Leibnitz.    Like- 
wise applicable  only  to  affirmative  syllogisms. 

3.  "  Prcedicatum  prcedicati  est  etiam  prcedicatum  subjecti."    A  trans- 
lation of  Aristotle's  first  antipredicamental  rule  (Categ.  iii).     The  fol- 
lowing may  be  regarded  as  a  free  rendering  of  this  excellent  form : 

4.  "  Whatever  predicate  is  universally  affirmed  or  denied  of  any 
middle  term  or  part  is  also  affirmed  or  denied  of  any  subject  contain- 
ed under  it." — Burgersdyck.     Applicable,  however,  only  in  extension. 

5.  "  Quicquid  de  omni  valet,  valet  etiam  de  quibusdam  et  singulis. 
Quicquid  de  nullo  valet,  nee  de  quibusdam,  nee  de  singulis  valet.1'' 
These  are  the  famous  "  Dicta  de  omni  et  nullo"  of  Aristotle,  as  drawn 
out  by  the  Latin  logicians  from  the  Prior  Analytics,  Part  1st,  i,  8. 

6.  "  Nota  notce  est  nota  rei  ipsius ;  et  repugnans  notaj,  repugnat  rei 
ipsi"     This  seems  especially  adapted  to  the  intensive  syllogism. 

7.  "  What  stands  under  the  condition  of  a  rule,  that  stands  also 
under  the  rule  itself." — Kant.     See  §  2,  last  paragraph. 


138  OF    REASONINGS. 

8.  "  In  so  far  as  two  notions  (notions  proper,  or  individuals)  either 
both  agree,  or,  one  agreeing,  the  other  does  not,  with  a  common  third 
notion,  in  so  far  these  notions  do  or  do  not  agree  with  each  other." 
This  is  Hamilton's  "  Supreme  Canon  for  the  "Unfigured  Syllogism,"  a 
form  we  will  briefly  consider  in  the  sequel. 

9.  "  What  worse  relation  of  subject  and  predicate  subsists  between 
either  of  two  terms  and  a  common  third  term,  with  which  one,  at 
least,  is  positively  related,  that  relation    subsists  between  the  two 
terms  themselves."    This  is  Hamilton's  "  Supreme  Canon  for  the  Fig- 
ured Syllogism." "     He  claims  for  it  perfection  of  statement  and  abso- 
lute generality,  it  being  the  principle  of  syllogisms  intensive  and  ex- 
tensive, positive  and  negative,  involving  any  of  the  eight  Hamiltonian 
judgments.9 

10.  "Any  notion  may  be  replaced  by  an  equivalent,  or  by  its  un- 
distributed genus,  or,  if  distributed,  by  any  of  its  parts."     We  pro- 
pose this,  believing  it  to  be  a  more  general  principle,  and  more  truly 
expressive  of  the  actual  process  of  thought  in  reasoning  than  some  of 
the  preceding.     It  is  simple  and  self-evident.     For  convenience  in 
reference,  we  will  call  it  the  Canon  of  Replacement.     Its  view  of  the 
syllogism  is  somewhat  peculiar.    It  considers  the  Sumption  as  declaring 
a  relation  between  two  notions ;  the  Subsumption  as  declaring  that 
some  other  notion  is  equivalent  to,  or  a  part  of,  one  of  these ;  the  syl- 
logistic judgment  as  being  the  substitution  of  that  for  this ;  and  the 
Conclusion  as  setting  forth  the  result.     Thus,  to  take  an  old  standard 
example,  "All  men  are  mortal;"  but  "Socrates  is  a  man,"  i.  e.,  he  is 
one,  a  part  of  "All  men."     So,  replacing  "All  men"  by  this  part, 
we  have  therefore  "Socrates  is  mortal."     This  Canon  will  apply  not 
only  to  all  reasonings  in  the  logical  whole,  but  also  to  those  in  the 
mathematical  whole.     For  example : 

A  is  equal  to  B ; 

B  is  equal  to  C ; 

.\  A  is  equal  to  C. 

This  most  simple  and  most  common  mathematical  syllogism,  which 
Dr.  Reid  said  could  not  be  subjected  to  any  of  the  approved  logical 

8  See  Logic,  p.  584  ;  and  Discussions,  pp.  604,  605.  See  also  the  Table  of  the 
Eight  Propositional  Forms  in  Part  3d,  iii,  §  3. 

"  Notwithstanding  the  high  pretensions*  of  this  Canon,  it  seems  that  Hamilton's 
own  "  Negative  Moods"  (Logic,  p.  679),  No.  li  a  and  b,  No.  v  a,  No.  vi  b,  No.  vii  a, 
No.  viii  6,  No,  xi  a  (Ferio\  and  No,  xii  b  are  in  direct  violation  of  it. 


THE    SYLLOGISM.  139 

canons,  and  hence  condemned  the  whole  science  and  art  of  Logic,  is 
obviously  a  very  simple  case  when  referred  to  the  Canon  of  Replace- 
ment. Moreover,  judgments  often  undergo  easy  modifications  which" 
are  difficult  to  express  in  strict  syllogistic  form  and  bring  under  com- 
mon logical  rules,  but  which  this  Canon  at  once  explains  and  justifies. 
For  an  example  we  take  the  famous  logical  puzzle  proposed  by  the 
Port-Royal  logicians,  which  they  solve,  not  very  clearly,  in  a  page 
and  a  half  of  discussion ;  which  Jevons  says  "  cannot  be  proved  by  the 
rules  of  the  syllogism  ;"  and  which  most  other  writers  omit  to  notice.10 

The  divine  law  commands  us  to  honor  kings  ; 
Louis  XIV  is  a  king; 
/.  The  divine  law  commands  us  to  honor  Louis  XIV.  , 

Its  solution  by  replacement  is  too  obvious  to  call  for  remark,  and 
seems  to  be  the  actual  mental  process  by  which  any  child  will  at  once 
accept  the  conclusion. 

§  5.  Aristotle's  dicta  are  directly  applicable  only  to  syllogisms  in 
the  first  figure.  For  this  reason,  and  also  because  the  application  as  a 
test  is,  in  some  cases,  somewhat  confusing,  logicians  have  resolved  the 
principle  of  the  syllogism  into  a  series  of  GENERAL  RULES  which  are 
applicable  to  all  figures ;  to  which  all  sound  reasonings  must  conform ; 
and  which,  being  quite  simple  and  applied  in  succession,  render  the 
process  of  testing  a  syllogism  easy,  quick,  and  sure.11  They  are  as 
follows : 

1.  A  syllogism  has  three,  and  only  three,  terms.  For  if  there  be 
four,  the  two  premises  can  have  no  common  term.  A  good  syllogism 
is  a  tripod.  The  following  is  a  quadruped ;  verbally  a  triad,  really  a 
Quaternio  Terminorum : 

Light  is  contrary  to  darkness ; 
Feathers  are  light ; 
/.  Feathers  are  contrary  to  darkness. 

10  See  UArt  de  Penser,  pt.  iii,  ch.  ix ;  and  Jevons'  Lessons  in  Logic,  p.  158. 

n  Hamilton  (Logic,  p.  215  sq.)  reduces  the  six  or  eight  Rules  to  three,  with 
an  acknowledged  sacrifice  of  their  generality,  and  with  a  sacrifice  also,  as  it  seems 
to  me,  of  their  perspicuity.  His  first  Rule  is  merely  our  1st  and  2d  stated  in 
one  compound  sentence.  But  why  condense  them  ?  The  very  intent  is  to  evolve 
from  the  canon  as  many  simple,  explicit  statements  as  are  needed  for  a  ready 
and  easy  test  of  the  validity  of  any  syllogism.  Of  course,  we  may  condense  them 
back  to  the  canon  itself,  without  displaying  much  ingenuity  or  obtaining  any 
advantage. 


140  OF    REASONINGS. 

2.  It  has  three,  and  only  three,  propositions.    For  three  terms  give 
three  pairs,  and  three  only,  without  repetition.     Apparently  we  have 
more  in  the  following  : 

All  beings  that  have  nerves  are  sentient =A 

All  self-moving  things  have  nerves = A 

Worms  are  self -moving =A 

.'.  Worms  are  sentient =  A 

The  reasoning  is  good,  and  the  form  logical ;  but  we  shall  hereafter 
find  that  it  is  a  Sorites,  resolving  into  two  syllogisms  of  three  propo- 
sitions each. 

3.  One  premise  at  least  must  Ibe  affirmative.    For  if  the  middle  term 
agrees  with  neither  of  the  other  two,  we  cannot  infer  through  it 
whether  or  not  they  agree  with  each  other.     From  these  premises, 

No  marble  is  sentient =E 

Some  statues  are  not  marble =0 

we  get  no  conclusion ;  however  true  it  may  be,  they  do  not  prove 
any  statue  not  sentient.  The  following,  however,  yields  a  conclusion : 

No  man  is  entirely  destitute  of  religious  feeling =E 

Many  men  are  not  true  believers  in  God =  1 

.*.  Many  who  are  not  true  believers  in  God  are  not  en- 
tirely destitute  of  religious  feeling =0 

But  the  minor  premise  is  really  an  affirmative,  the  negative  particle 
being  treated  as  belonging  to  the  predicate,  which  thereby  becomes 
equivalent  to  "  infidels,"  and  constitutes  the  subject  of  the  conclusion. 

4.  If  one  premise  is  negative,  the  conclusion  must  be  negative. 
For  if  one  term  is  denied  to  the  middle,  it  must  be  denied  finally  to 
the  other  term  which  agrees  with  the  middle  by  Rule  3.     E.  g. : 

Few  men  weep =0 

All  men  feel =  A 

We  cannot  conclude,  "Some  who  feel  weep."  However  obviously  true 
it  may  be,  these  premises  do  not  yield  it.  "  Few  "  is  essentially  neg- 
ative, and  rightly  construed  gives  us  a  negative  sumption,  yielding  a 
negative  conclusion ;  thus, — 

Sumption, Most  men  do  not  weep =0 

Now  subsume, All  men  feel =A 

Hence  we  conclude, . .  Many  who  feel  do  not  weep =0 

5.  The  middle  term  must  be  distributed  at  least  once.     For  if  in 

each  premise  it  is  used  in  a  partial  sense,  it  may,  in  each,  denote  dif- 


THE    SYLLOGISM.  141 

ferent  objects,  and  so  be  equivalent  to  two  terms,  making  four  in  all, 
in  violation  of  Kule  1.  From  these  premises. 

Some  of  our  citizens  use  profane  language =1 

Some  of  our  citizens  are  refined  gentlemen =1 

we  can  conclude  nothing,  for  the  middle  evidently  refers  to  entirely 
different  groups  of  persons.  This  logical  fault  is  called  the  fallacy  of 
Undistributed  Middle.  Sometimes  it  is  not  quite  so  very  obvious; 
for  example, — 

A  valid  syllogism  has  three  terms —A 

This  syllogism  has  three  terms =  A 

.'.  This  is  a  valid  syllogism =A 

Here  the  middle  is  in  each  case  the  predicate  of  an  affirmative,  and 
hence  is  not  distributed;  and  therefore  the  stated  conclusion  is  un- 
proven.  Even  when  the  portions  of  the  middle  are  the  same,  a  con- 
clusion is  not  competent  unless  that  fact  be  declared,  which  virtually 
makes  the  portion  a  total.  For  example, — 

Some  paper  currency  is  legal  tender z=I 

Government  notes  are  paper  currency =A 

From  these  no  conclusion  is  competent ;  but  we  may  happen  to  know, 
and  think  it  thus, — 

All  of  a  certain  portion  is  legal  tender =A 

Government  notes  are  that  portion =  A 

.*.  Government  notes  are  legal  tender —A 

If,  however,  the  undistributed  middle  term  be  so  quantified  that 
the  sum  of  the  two  portions  is  more  than  the  whole,  a  conclusion  is 
competent.  This  Hamilton  calls  the  "Ultra-total  Quantification  of 
the  Middle  Term."  For  example, — 

Two  thirds  of  mankind  are  Asiatics =1  Asiatics 


Two  thirds  of  mankind  are  heathen =1  mankind 

.*.  Some  heathen  are  Asiatics =1  — ' — 

(At  least  one  half  are  Asiatics,  perhaps  all  are. )  heathen 


One  other  example  will  suffice : 

Very  few  men  have  never  prayed =0 

Nearly  all  men  are  far  from  being  saints =  1 

.'.  Many  who  are  far  from  being  saints  have  (not  never)  prayed..  =0 

The  old  Logic  makes  no  provision  for  this  exception  to  the  rule ;  and 
it  is  manifest  that  the  reasoning  is  mathematical  rather  than  logical. 


142  OF    REASONINGS. 

6.  Ail  extreme  particular  in  a  premise  must  be  so  in  the  conclusion. 

For  if  only  some  is  premised,  wo  cannot  conclude  all ;  we  cannot 
argue  from  part  to  whole.  The  violation  of  this  rule  is  called  the 
fallacy  of  Illicit  Process.  It  is  called  Illicit  Major  or  Illicit  Minor, 
according  to  the  term  to  which  the  fault  attaches.  Here  is  an  obvi- 
ous example : 

All  birds  are  winged =A 

A  bat  is  not  a  bird =E 

.*.  A  bat  is  not  winged =E 

The  major  term,  "  winged,"  is  not  distributed  (i.  e.,  is  particular)  in  the 
premise,  since  it  is  there  the  predicate  of  an  affirmative,  but  it  is  dis- 
tributed (i.  e.,  is  universal)  in  the  conclusion,  since  it  is  there  the  pred- 
icate of  a  negative,  proposition.  Hence  there  is  an  illicit  process  of 
the  major  term.  The  following,  not  quite  so  obvious,  is  an  illicit  proc- 
ess of  the  minor  term : 

Persons  without  imagination  are  not  true  poets =E 

Good  logicians  are  often  without  imagination =  I 

.*.  Good  logicians  are  not  true  poets =E 


There  are  two  useful  rules  which  are  deduced  from  those  preceding, 
and  might  be  appended  as  corollaries ;  but  we  will  state  them  co-ordi- 
nately. 

7.  From  two  particulars  there  can  be  no  conclusion.  For  if  the 
premises  be  1 1,  there  is  no  distributed  term  for  a  middle,  Rule  5.  If 
they  be  00,  both  premises  are  negative,  Rule  3.  If  they  be  I O  or  OI, 
there  is  but  one  term  distributed,  the  predicate  of  O ;  if  this  be  taken 
for  the  middle  term,  then  illicit  major,  since  the  negative  conclusion 
required  by  Rule  4  distributes  its  predicate,  the  major  term ;  if  it  be 
not  so  taken,  then  undistributed  middle,  Rule  5.  E.  g. : 

Some  students  row  well =1 

Some  study  well =1 

(No  conclusion.) 

Some  students  are  not  card-players =0 

Some  are  not  church-goers =0 

(Xo  conclusion.) 

Some  students  do  not  waltz =0 

Some  "  Germans  "  are  students - —  I 

(Nothing  follows.) 


THE    SYLLOGISM.  143 

8.  If  one  premise  is  particular,  the  conclusion  must  be  so.     For  a 

universal  conclusion  following 

A I  would  require  2  distributed  terms ;  there  is  but  one ; 
AO      "  "3          "  «          "     are  but  two; 

jjj       «  "3  "  "  "       "      "      " 

EO,  both  negative,  Rule  3. 

Aldrich,  in  close  imitation  of  Petrus  Hispanus,  gives  the  following 
summary  of  his  rules : 

"Distribuas  medium  ;  nee  quartus  terminus  adsit; 
Utraque  nee  praemissa  negans,  nee  particularis  ; 
Sectetur  partem  conclusio  deteriorem ; 
Et  non  distribuat,  nisi  cum  praemissa,  negetve." 


144  OF   REASONINGS. 


II.  FIGURE  AND  MOOD. 

§  1.  Syllogisms  are  divided  into  Figures  according  to  the  position 
of  the  middle  term.  In  the  First  Figure  it  is  the  subject  of  the  major 
premise,  and  predicate  of  the  minor.  In  the  Second,  it  is  the  predi- 
cate of  both  premises.  In  the  Third,  it  is  the  subject  of  both.  In 
the  Fourth,  it  is  the  predicate  of  the  major  premise,  and  subject  of 
the  minor.  Thus : 


Fig.  1. 

Fig.  2. 

Fig.  3. 

rig.  *. 

M^P 

P-^M 

M  —  P 

P  —  M 

S^M 

S^M 

M—  S 

M^S 

/.  S  —  P 

.'.  S  ^  P 

.'.  S  —  P 

/.  S  —  P 

This  last  line  is  a  useful  mnemonic,  without  other. meaning.  The  no- 
tion of  "  Figure"  was  borrowed  by  Aristotle  from  Figures  of  Rhetoric, 
which  are  departures  from  the  plain,  literal  forms  of  speech.  On 
this  analogy,  there  ought  to  be  some  one  standard  form  from  which 
all  others  are  departures,  and  thence  properly  called  Figures.  Such 
standard  form  is  the  misnamed  First  Figure,  which  is  the  pure  type  of 
deductive  argument.1 

Each  of  these  figures  may  claim  to  have  its  special  Canon.  Aris- 
totle's dicta  de  omni  et  nullo  are  specially  adapted  to  the  first  figure. 
It  is  easy  to  modify  the  phraseology  so  as  to  adapt  them  in  turn  to 
each  of  the  others.  But  this  cumbers  us  with  four  canons  instead  of 
one,  and  to  no  advantage.  We  will,  then,  let  them  go  canonless,  and 
subsequently  show  that  the  last  three  may  be  reduced  to  the  first. 
There  are,  however,  special  rules  governing  the  figures,  deduced  from 
the  general  rules  of  the  syllogism,  to  which  it  is  well  to  give  some  at- 
tention. They  follow,  illustrated  by  an  example. 


, figuras  syllogismorum,  quce  dicuntur  (Appuleius  'formulas'  vocat), 
ab  Aristotele  appellatas  esse  lul.  Pacius  putat,  quia  figuris  geometricis  adscriptis 
syllogismi  ab  eo  illustrati  sint.  Equidem  hanc  vocem  non  tarn  a  geometris  peti- 
tam  quam  de  ipso  ordine  termmorum  accipiendam  putaverim,  quern  o-^^/ia  appel- 
lari  licebit,  etiam  si  de  geometricis  figuris  non  cogitetur."  (Waitz,  Com.  on  Organ., 
26  b  33.)  But  Hamilton,  per  contra,  maintains  the  opinion  of  Pacius. 


FIGURE  AND  MOOD.  145 

CONSPECTUS  OF  FIGURE. 

Example.  Special  Rules. 

Fig.  1  (subprce). 

No  man  is  perfect Mnjor  premise  must  be  universal.   (Else  undistrib.  middle.) 

.Some  saints  are  men Minor  premise  must  be  affirmative.    (Else  illicit  major.) 

.".  Some  saints  arc  not  perfect. 

Fig.  2  (prce  prce). 

No  perfect-one  is  a  man. . .  .Major  premise  must  be  universal.    (Else  illicit  major.) 
Some  saints  are  men One  premise  must  be  negative.    (Else  uudistrib.  middle.) 

.*.  Some  saints  are  not  perfect.    (Hence  the  conclusion  is  always  negative,  Rule  4.) 

Fig.  3  (sub  sub). 

No  man  is  perfect. 

Some  men  are  saints Minor  promise  must  be  affirmative.    (Else  illicit  major.) 

.'.  Some  saints  are  not  perfect.    Conclusion  must  be.particular.     (Else  illicit  minor.) 

Fig.  4  ( prce  sub). 

No  perfect-one  is  a  man. .  .  .If  either  prem.  is  neg..  maj.  must  be  univ.  (Else  ill.  maj.) 
Some  men  arc  saints If  maj.  prcm.  is  aft". ,  rnin.  must  be  univ.  (Else  uudis.  mid. ) 

.*.  Some  saints  are  not  perfect.If  min.  prem.  is  aff.,  conclu.  must  be  partic.  (Else  ill.  min.) 

These  rules  and  their  grounds  should  be  thoroughly  examined ;  but 
only  those  of  the  first  figure  need  be  retained  in  memory.  All  have 
reference  to  extension.  To  adapt  them  to  the  intensive  syllogism,  it 
is  needful  only  to  change  the  word  "major"  to  "minor"  and  vice 
versa,  wherever  they  occur.  The  symbolic  notation  of  the  example 
above  (in  extension)  is  the  same  for  each  of  the  four  figures;  the 
graphic  notation  is  different  for  each  of  the  figures ;  thus : 


Perfect 


Men 


I  Saints 


^-,S      (Fig.  1.) 


§  2.  Quite  a  number  of  recent  logicians  insist  that  the  varia- 
tions of  the  syllogism  by  figure  are  arbitrary,  simply  serving  to  dis- 
play the  middle  term  in  all  possible  positions.  They  endeavor  to 
prove  that  reasoning  in  either  of  the  last  three  is  distorted  and  un- 
natural, and  that  the  first  only  is  the  natural  order  of  thought.  Kant 
himself,  in  a  little  tract  on  the  question,  followed  by  Hamilton  in  ex- 
tenso,  contends  that  all  reasoning  is  actually  in  the  first  figure ;  for, 
when  perforce  it  is  expressed  in  one  of  the  others,  the  mind  interpo- 
lates the  converse  of  one  at  least  of  the  propositions,  and  thus  men- 
tally reduces  it  to  the  first  figure,  which  alone  is  pure  and  natural.  This 
is  possible  to  conceive,  but  perhaps  impossible  to  prove.  We  readily 

10 


146  OF    REASONINGS. 

grant,  however,  that  a  reasoning  which  in  the  first  figure  is  orderly  and 
natural  will,  when  reduced  to  another,  appear  distorted,  awkward,  and 
unnatural.  Indeed,  the  example  given  above  sufficiently  illustrates  the 
fact.  But  it  seems  that  the  same  is  true  of  the  second  and  third ; 
that  there  are  reasonings  which  naturally  appear  in  one  or  the  other 
of  these  two  figures,  and  that  these,  when  reduced  to  the  first,  become 
harsh  and  disordered.  We  will  briefly  consider  these  two,  deferring 
until  later  an  examination  of  the  fourth  figure. 

It  is  hardly  to  be  questioned  that  the  natural  order  of  predication 
is  that  which  predicates  a  greater  of  a  less,  as  a  genus  of  a  species. 
How  much  better  to  say  "  Some  scents  are  pleasant"  than  to  say 
"Some  pleasant  things  are  scents."  Now  there  is  nothing  in  the 
nature  of  a  negative  proposition  that  determines  the  relative  extent 
of  its  two  terms ;  but  if  we  happen  to  know  that  one  is  wider  than 
the  other,  we  naturally  make  that  the  predicate ;  and  if  it  be  the 
middle  term,  the  reasoning  will  naturally  fall  in  the  second  figure,  be- 
cause then  it  will  be  the  predicate  in  both  premises.  E.  g. : 

The  true  apostles  were  not  thieves ; 
Judas  was  a  thief ; 
.'.  Judas  was  not  a  true  apostle. 

By  converting  the  major  premise  to  "  No  thieves  were  true  apostles," 
we  get  the  first  figure,  but  sacrifice  the  smooth  natural  order  of  state- 
ment as  given  in  the  second  figure. 

On  the  other  hand,  if  what  we  know  to  be  the  narrower  of  the  two 
terms  of  a  negative  proposition  is  the  middle  term,  the  reasoning  will 
naturally  fall  in  the  third  figure,  because  then  it  will  be  the  subject  of 
both  premises.  E.  g. : 

The  apostles  sought  no  temporal  reward ; 
The  apostles  were  zealous  in  their  work ; 
/.  Some  zealous  persons  did  not  seek  temporal  reward. 

By  converting  the  minor  premise  to  "Some  zealous  persons  were 
apostles,"  we  get  the  first  figure,  but  manifestly  lose  the  smooth  nat- 
uralness of  the  given  expression. 

So,  then,  we  conclude  with  Thomson  that,  since  in  some  cases  nat- 
ural reasons  prescribe  the  second  or  third  figure  and  reject  the  first, 
the  distinction  of  these  is  not  an  arbitrary  variation,  but  a  true  ex- 
pression of  the  mental  act.2 

9  See  Outline,  §  95. 


FIGURE    AND    MOOD.  147 

Let  us  append  that  while  either  of  the  four  forms  of  the  proposi- 
tion may  be  concluded  in  the  first  figure,  it  seems  especially  suited  to 
establishing  general  propositions ;  the  universal  affirmative  A  can  be 
proved  only  in  this  figure.  In  its  two  affirmative  forms  the  predi- 
cates are  always  thought  as  greater  wholes  than  the  subjects.  But 
sometimes  a  previous  thought,  a  special  purpose  in  view,  may  deter- 
mine us  to  prefer  to  mate  the  greater  whole  the  subject,  and  this  also 
will  often  throw  the  reasoning  in  the  second  or  third  figure  rather 
than  the  first.  The  second  figure,  whose  conclusion  is  always  nega- 
tive, seems  especially  adapted  for  proving  differences  in  things,  and 
clearing  obscure  thought.  Hence  its  principle — that  if  one  term  is 
contained  under  and  another  excluded  from  a  third,  they  exclude 
each  other — :is  called  the  dictum  de  di verso*  The  third  figure,  whose 
conclusion  is  always  particular,  seems  specially  adapted  for  bringing 
in  examples,  and  thus  proving  an  exception  to  some  universal  state- 
ment. Its  principle  is  that  two  terms  which  contain  a  common  part, 
partially  agree ;  or  if  one  contains  a  part  which  the  other  does  not, 
they  partially  differ.  This  is  called  the  dictum  de  excmplo.  E.  g. : 

Tweed  was  not  an  honorable  man  ; 
Tweed  possessed  high  intellectual  culture  ; 
/.  Some  one  at  least  of  high  culture  was  not  honorable. 

This  conclusion  is  the  contradictory  of  "  All  of  high  intellectual  cult- 
ure are  honorable,"  and  overthrows  it.  Hence  the  third  figure  is  well 
suited  to  disprove  A,  and  also  E. 

The  middle  term  in  the  example  is  individual.  Such  a  case  can  occur 
only  in  Fig.  3  ;  for  in  either  of  the  others  the  middle  term  is  once  at 
least  a  predicate,  and  an  individual  cannot  become  a  predicate.  This 
alone  establishes,  not  merely  the  naturalness  and  propriety,  but  the 
necessity,  of  this  figure.  Moreover  we  remark  that  while  the  middle 
term  is  essentially,  and  hence  always,  the  medium  of  comparison,  it  is 
only  in  affirmative  syllogisms  of  the  first  figure  that  it  is  necessarily 
of  intermediate  extent.  But  some  of  the  logicians  referred  to  above, 
as  Bain  and  Bowen,  involve  in  their  objections  to  the  second  and 


8  Says  Whately  (Loyic,  p.  101),  "The  arguments  used  in  the  process  called 
Abscissio  injiniti  will,  in  general,  be  most  easily  referred  to  this  figure.  The  phrase 
is  applied  to  a  series  of  arguments  in  which  we  go  on  excluding  one  by  one  certain 
suppositions  or  certain  classes  of  things  from  that  whose  real  nature  we  are  seek- 
ing  to  ascertain." 


148  OF   REASONINGS. 

third  figures  the  notion  that  the  middle  term  ought  to  be  always  of 
intermediate  extent.  This  is  mere  confusion  of  thought  as  to  what 
is  meant  by  "  middle,"  and  their  objections  are  unsound/ 

§  3.  The  four  figures  of  the  syllogism  are  subdivided  into  Moods, 
upon  the  ground  of  the  quantity  and  quality  of  the  premises.  The 
conclusion  need  not  be  taken  into  account,  since  its  quantity  and  qual- 
ity are  determined  by  the  premises.  The  method  for  determining 
the  moods  is  as  follows : 

Relative  to  quantity  and  quality,  we  recognize  four  propositions, 
A,  E,  I,  0.  These,  as  premises,  taken  two  at  a  time,  yield  sixteen 
possible  combinations,  exhibited  in  the  following  scheme : 


AA 

Figs.  1 

,3,4. 

EA 

Figs.  1, 

2,3,4. 

IA 

Figs.  3,  4 

OA 

Fig.  3. 

AE 

" 

2,4. 

[EE] 

3d  Gen.  Rule. 

[IE] 

6th  Gen. 

Rule. 

[OE] 

3d  Gen.  Rule. 

AI 

" 

1,3. 

El 

Figs.  1, 

2,  3,  4. 

[II] 

7th  '  " 

it 

[01] 

7th  " 

u 

AO 

M 

2 

[EO] 

3d  Gen 

.  Rule. 

[10] 

7th     (i 

" 

[00] 

3d    " 

" 

But  not  all  these  combinations  will  yield  conclusions,  i.  c.,  they  do 
not  represent  the  premises  of  valid  syllogisms.  Those  bracketed  are 
to  be  eliminated  as  violative  of  General  Rules  (i,  §  5).  Eight — one 
half — remain  as  valid,  since  they  accord  with  the  General  Rules.  In 
reference  to  IE,  we  may  remark  that  its  conclusion  must  be  negative, 
by  Rule  4 ;  the  predicate  of  this  conclusion,  the  major  term,  is  there- 
fore distributed ;  but  the  major  premise  I  has  neither  tenn  distributed, 
which  violates  Rule  6,  giving  illicit  major. 

Let  us  now  inquire  in  which  of  the  four  figures  each  of  these  eight 
valid  combinations  may  occur.  We  apply  the  Special  Rules  (§  1),  and 
find  that  EA  and  El  accord  with  all  these  rules,  and  therefore  can  appear 
in  each  of  the  four  figures,  as  indicated  in  the  scheme.  The  figures 
in  which  the  others  can  appear  are  similarly  ascertained  and  indicated. 
Upon  counting,  we  find  there  are  nineteen  valid  Moods  of  the  Syllogism. 

§  4.  The  first  figure  exhibits  four  moods,  AA,  EA,  AI,  El.  Let  us 
now  annex  to  each  of  these  the  symbol  of  the  conclusion  it  necessi- 
tates, and  coin  a  word  containing  these  three  vowels  in  their  order, 
as  the  name  of  that  mood,  thus:  Barbara,  Celarcnt,  Darii,  Ferio. 

4  "  Major  terminus  appellatur  in  secunda  figura  qui  mcdio  proprior,  minor  qui 
remotior  est  ab  eo."  (Waitz,  26  b  37.)  With  Aristotle  the  relations  of  the  terms, 
not  their  arbitrary  position,  fixes  the  figure.  Cf.  Trendelcnburg,  Elem.  §  28. 


FIGURE    AND    MOOD.  149 

The  moods  of  the  other  three  figures  are  treated  in  the  same  way, 
and  the  names  of  the  nineteen  moods  thus  coined  are  arranged 
in  the  following  MNEMONIC  HEXAMETERS,  which  the  learner  should 
carefully  commit  to  memory  : 

Fig.  1  =  Barbara,  Celarent,  Darii,  Fevio  que  priori*  ; 
Fig.  2  =  Cesare,  Camestres,  Festino,  Baroco 1  secundcc  ; 
Fig.  3  =  Tertia  Darapti,  Disamis,  Datisi,  Felapton, 

Bocardo,2  Ferison  habet.     Quarto,  insuper  addit 
Fig.  4  —  Bramantip,  Camenes,  Diraaris,  Fesapo,  Fresison. 

2 — or  Dokainok.  1 — orFakofo. 

These  names  of  the  nineteen  valid  moods  are  exceedingly  convenient. 
By  applying  its  name  to  any  reasoning,  we  at  once  indicate  its  figure, 
and  the  quantity  and  quality  of  each  proposition,  and  also,  as  will  be 
seen  now  directly,  its  relation  to  other  moods  to  which  it  may  be  re- 
duced, and  the  method  of  reduction.  Moreover,  they  constitute  a  test ; 
for,  since  these  are  all  the  valid  moods,  whenever  we  have  a  simple 
syllogistic  form  to  which  none  of  these  names  is  applicable,  we  know 
at  once  that  the  reasoning  is  false. 

It  may  be  well  to  mention  here  that  had  we  taken  the  conclusion 
into  account  in  developing  the  valid  moods,  we  should  have  found  in 
Fig.  1  two  others,  viz.,  AAI  and  EAO ;  in  Fig.  2  two  others,  viz., 
EAO  and  AEO ;  and  in  Fig.  4  one  other,  viz.,  AEO.  These  are 
valid,  indeed,  but  superfluous ;  for  it  will  be  observed  that  the  con- 
clusion in  each  is  particular,  although  the  premises  warrant  a  univer- 
saL  They  are  called  the  "  Subaltern  moods,"  or  "  Moods  of  a  weak- 
ened conclusion."  It  is  not  needful  to  take  them  into  consideration. 

In  noting  the  conclusions,  it  will  be  seen  that  each  of  the  four  judg- 
ments is  proved  in  Fig.  1.  Its  four  moods,  however,  are  obviously 
reducible  to  two,  the  third  and  fourth  being  unessential  varieties  of 
the  first  and  second.  Thus : 

Barbara  or  Darii.  Celarent  or  Ferio. 

AllMisP;  NoMisP; 

All  or  some  S  is  M ;  All  or  some  S  is  M ; 

.*.  All  or  some  S  is  P.  /.  No  S  is  P, 

or  Some  S  is  not  P. 

Here  is  one  positive  and  one  negative  form.  Since  all  the  other 
moods  may,  as  we  shall  find,  be  reduced  to  one  or  the  other  of  these, 
they  are  the  two  fundamental  forms  of  all  reasoning. 


150  OF    REASONINGS. 

Again,  in  noting  the  conclusions  throughout  it  will  be  further 
seen  that — 

A  is  proved  in  1  figure  and  in  1  mood,  whose  initial  letter  is  B. 

E  "  3  figures       "     4  moods,     "         "  "        C. 

I  "  3  figures       "     6  moods,     "          "  "        D.1 

0  "  4  figures       "     8  moods,     "          "  "        F.3 

1  Except  Bramantip.  3  Except  Baroco  and  Bocardo. 

Hence,  says  Aristotle,  the  proposition  A  is  the  hardest  to  establish 
and  the  easiest  to  overthrow ;  and  O  is  the  easiest  to  establish  and 
the  hardest  to  overthrow.  In  general,  universals  are  more  easily  over- 
thrown ;  particulars  more  easily  established. 

§  5.  We  are  now  to  consider  REDUCTION.  It  is  usually  stated  as  of 
two  kinds.  First,  then,  Ostensive  Reduction.  A  syllogism  in  any 
mood,  except  the  first  four,  may  be  ostensively  reduced  to  one  or  the 
other  of  these.  The  initial  consonant  in  each  name  is  the  same  as 
that  of  the  mood  in  Fig.  1  to  which  it  reduces.  Or,  more  generally, 
equivalent  moods  have  the  same  initial  letter.  We  must  except  Baroco 
and  Bocardo,  or,  rather,  consider  them  replaced  by  their  alternates 
Fakofo  and  Dokamok.  The  reduction  is  accomplished  by  substitut- 
ing for  one  or  both  of  the  premises  an  immediate  inference  from  it. 
Other  consonants  in  the  name  of  a  mood  direct  us  in  doing  this. 

s  indicates  that  the  proposition  symbolized  by  the  vowel  that  pre- 
cedes it  is  to  be  converted  simply. 

p  indicates  that  the  preceding  proposition  is  to  be  converted  per 
accidens.  (Except  in  Bramantip,  where  it  shows  that,  after  con- 
verting simply,  a  universal  is  warranted  by  the  premises.  This  is 
just  the  reverse  of  per  accidens,  which  reduces  quantity.) 

k  indicates  conversion  by  contraposition. 

f  indicates  infinitation. 

m  indicates  that  the  premises  are  to  be  transposed  (mutari). 
The  consonants  b,  d,  1,  n,  r,  t,  are  not  significant,  but  are  inserted 
merely  for  the  sake  of  euphony,  or  for  metrical  quantity. 

An  exceptive  remark  is  needful  here.  If  in  a  given  syllogism  the 
premise  requiring  conversion  in  order  to  reduction  is  an  individual 
proposition,  then  the  reduction  is  not  practicable ;  for  an  individual 
proposition  cannot  be  converted.  This  consideration  makes  clear,  not 
merely  the  propriety  of  figures  other  than  the  first,  but  their  neces- 
sity, since  many  of  our  reasonings  involving  individual  propositions 
cannot  be  expressed  in  the  first  figure. 


FIGURE    AND    MOOD.  151 

The  following  examples  will  sufficiently  illustrate  the  process : 

Fig.  2,  Camestres,  reduces  to  Fig.  1,  Cdarent. 

All  P  is  M ;  No  M  is  S  ; 

NoSisM;  AllPisM; 

.'.  No  S  is  P.  /.  No  P  is  S. 

Cam-  Every  wicked  man  is  discont'd;    \        f   Ce-   No  discontented  man  is  happy; 
es-     No  happy  man  is  discontented ;     >  =  -|    la-    Every  wicked  man  is  discont'd ; 
tres.    .'.  No  happy  man  is  wicked.          )        (rent.  /.  No  wicked  man  is  happy. 

Fig.  3,  Darapti,  reduces  to  Fig.  1,  Darii. 

Da-     All  wits  are  dreaded ;  \        r  Da-   All  wits  are  dreaded ; 

rap-    All  wits  are  admired;  >  =  •<   ri-     Some  who  are  admired  are  wits; 

ti.  .'.  Some  who  are  adm'd  are  dreaded. )        (    i.  .'.  Some  who  are  adm'd  are  dreaded. 

Fig.  2,  Fakofo,  reduces  to  Fig.  1,  Ferio. 

Fak-   All  murders  are  intentional;  \        f  Fe-    No  unintent'l  things  are  murders; 

Of-     Some  homicides  are  not  intent'l ;   >  =  -J  ri-     Some  homicides  are  unintent'l ; 
O.  .'.  Some  homicides  are  not  murders.  )        (  o.  .'.  Some  homicides  are  not  murders. 

The  ostensivc  reduction  now  explained  could  not,  it  was  believed, 
be  applied  to  the  two  moods  named  Baroco  and  Bocardo.  Hence  the 
old  logicians  devised  for  them  what  they  describe  as  a  second  kind  of 
reduction,  the  JReductio  ad  impossibile.  It  is  intended  as  a  test  of  the 
validity  of  reasoning  from  granted  premises  in  these  two  moods. 

B,  the  initial  letter,  shows,  not  that  the  reasoning  is  reduced  to  Bar- 
bara, but  that  Barbara  is  used  in  making  the  test. 

c  indicates  that  the  proposition  preceding  it  is  to  be  omitted,  and 
the  contradictory  of  the  conclusion  substituted.  This  gives  prem- 
ises in  Barbara,  from  which  a  new  conclusion  is  drawn.  E.  g. : 

Fig.  2,  Baroco,  is  tested  by  Fig.  1,  Barbara. 

Ba-  All  murders  arc  intentional ;  (1)  Bar-  All  murders  are  intentional;  (4) 
roc-  Some  homicides  are  not  intent'l ;  (2)  \S  ba-  All  homicides  are  murders;  (o) 
O.  .'.  Some  homicides  are  not  murders.  (3)/\  ra.  .'.  All  homicides  are  intent'l.  (6) 

Here  the  conclusion  drawn  in  Barbara  (6)  is  false,  because  it  contra- 
dicts a  granted  premise  (2).  Hence  a  premise  in  Barbara  is  false. 
But  one  of  these  (4)  having  been  granted  (1),  the  false  one  must  be 
the  one  substituted  (5).  Now  this  false  proposition  being  the  con- 
tradictory of  the  original  conclusion  (3),  that  conclusion  must  be  true, 
and  this  reasoning  in  Baroco  valid.  So  also  tho  following : 

Fig.  3,  Bocardo,  is  tested  by  Fig.  1,  Barbara. 

Boc-    Most  men  do  not  weep ;  (2)  *    *Bar-   All  who  feel  weep ;  (5) 

ar-      All  men  feel;  (1)  V  ba-     All  men  feel;  (4) 

do.  .'.  Many  who  feel  do  not  weep,    (3)  /  \  ra, .',  AH  men  weep.         (6) 


152  OP   REASONINGS. 

This  process  seems  to  be  sufficiently  simple  and  obvious.  But  the 
mood  Bocardo  was  famous  in  the  schools,  and,  even  more  than  Baroco, 
was  the  opprobrium  of  the  scholastic  system  of  reduction.  Says 
Hamilton,  "  So  intricate,  in  fact,  was  this  mood  considered  that  it  was 
looked  upon  as  a  trap,  into  which  if  you  once  got,  it  was  no  easy  mat- 
ter to  find  an  exit.  Bocardo  was,  during  the  Middle  Ages,  the  name 
given  in  Oxford  to  the  Academical  Jail,  or  Career,  for  refractory  stu- 
dents,— a  name  which  still  remains  as  a  reliquc  of  the  ancient  logical 
glory  of  that  venerable  seminary."  Perhaps  the  perplexity  arose  some- 
what from  the  process  being  considered  and  named  as  a  kind  of  re- 
duction. Many  logicians  of  the  present  day  continue  to  speak  of  it 
as  "indirect  reduction."  But  obviously  it  is  not  a  reduction  at  all, 
and  to  call  it  so  is  mere  confusion.  It  is,  as  already  indicated,  only 
an  indirect  test  of  the  validity  of  the  reasoning  when  it  occurs  in  these 
moods.  And  it  may  be  well  to  add  that  all  the  other  moods  can  be 
tested  by  the  same  process.  This  is  elaborately  but  uselessly  exhib- 
ited by  Schuyler.5 

But  the  test,  even  in  the  case  of  Baroco  and  Bocardo,  is  of  no  prac- 
tical value,  and  is  superfluous.  We  have  inherited  it  from  the  old 
logicians,  who,  as  has  been  said,  supposed  that  these  two  moods  could 
not  be  ostensively  reduced.  In  this  they  were  mistaken.  Mark  Dun- 
can, as  early  as  1612,  and  after  him  Noldius,  in  1666,  showed  that  by 
the  use  of  contraposition  Baroco  could  be  reduced  to  Ferio,  and  Bo- 
cardo to  Darii.  Noldius  proposed  to  call  the  former  Facrono,  and 
the  latter  Docamroc.  Whately  called  attention  to  this  method,  but 
did  not  observe  a  defect  in  the  name  Facrono,  and  rendered  the  other 
defective  by  omitting  the  terminal  letter.  Hamilton  recognizes  that 
the  reduction  may  be  made,  but  blunders  sadly  in  the  attempt  to  re- 
duce Baroco,  which  his  editor  admits.6  We  have  proposed  the  names 
Fakofo  and  Dokamok  as  alternates,  or  as  substitutes,  and  have  already 
exhibited  in  an  example  the  reduction  of  the  former  to  Ferio.  The 
admission  of  these  substitutes  would  not  affect  the  metre  of  the  mne- 
monic lines,  and  we  could  then  dismiss  from  technical  Logic  this 
operose,  indirect,  and  practically  useless  test  per  impossibile. 

The  Latin  mnemonic  hexameters,  it  must  be  confessed,  are  a  marvel 
of  ingenuity.  De  Morgan  calls  them  "  magic  lines,  more  full  of  mean- 
ing than  any  others  that  ever  were  written."  Hamilton  calls  them 
"  cabalistical  verses,"  and  says  that  "  taking  them  on  their  own 

6  Logic,  pp.  75-77.  6  Logic,  pp.  313-14. 


FIGURE    AND    MOOD.  153 

ground,  there  are  few  human  inventions  which  display  a  higher  in- 
genuity." They  were,  so  far  as  relates  to  the  first  three  figures,  the 
invention  of  Petrus  Hispanus,  already  referred  to  as  the  author  of  the 
prepositional  symbols.  He  was  a  native  of  Lisbon,  became  Pope 
John  XXII  in  1277,  and  died  the  same  year.  The  corresponding  Greek 
lines  are  much  less  ingenious,  as  the  names  of  the  moods  in  them 
mark  only  the  order,  the  quantity,  and  the  quality  of  the  propositions, 
not  indicating  any  method  of  reduction,  and,  indeed,  not  even  the 
equivalent  moods.  They  were  the  invention  of  Nicephorus  Blem- 
midas,  who  was  nominated  Patriarch  of  Constantinople.  Which  had 
priority  in  this  invention  is  uncertain.  It  is  curious,  however,  to  note 
that  these  two  logicians  attained  the  two  highest  places,  the  one  in 
the  Roman,  the  other  in  the  Greek  hierarchy ;  but  as  the  one  had 
hardly  begun  to  reign  when  he  was  killed  by  the  fall  of  his  palace,  so 
the  other,  declining  the  nomination,  did  not  enter  on  the  office  at  all. 
The  several  works  of  the  Pope  and  the  Patriarch  were  for  many  cen- 
turies the  text-books  on  Logic,  the  one  in  the  Latin,  the  other  in  the 
Greek  schools.7 

But  it  may  very  properly  be  asked,  why  should  we  have  reduction  ? 
Reasoning  certainly  does  not  become  more  cogent  by  being  reduced 
to  the  first  figure ;  but,  says  Bowen,  it  becomes  more  elegant  and  per- 
spicuous. That  depends  on  whether  a  given  case  naturally  belongs  in 
the  first  figure.  If  so,  then  this  is  true.  But  if  the  case  naturally  be- 
longs in  some  other  figure,  then  its  reduction  to  the  first  renders  it 
more  or  less  awkward  and  obscure.  The  answer  more  usually  given 
assumes  that  the  system  of  reduction  is  a  method  for  testing  the  va- 
lidity of  reasonings.  As  the  dicta  of  Aristotle  arc  directly  applicable 
only  to  the  first  figure,  instead  of  inventing  other  dicta  for  the  other 
figures,  we  reduce  them  to  the  first,  and  then  apply  the  dicta  de  omni 
et  nullo.  Thus  we  become  assured  of  the  validity  of  our  reasoning, 
and  any  fallacies  in  it,  which  might  otherwise  escape  notice,  become 
at  once  apparent.  This  answer  is  clear,  but  unsatisfactory.  It  views 
Logic  as  an  art.  If  such  be  the  object  of  reduction,  it  is  not  worth 
an  hour's  study ;  for  in  actual  argumentation  this  test  is  never  used 
by  the  initiated,  and  the  uninitiated  never  err  for  lack  of  it.  The 
mind  practically  grasps  with  more  ease  an  argument  in  its  familiar 
condensed  modes  of  presentation,  and  sees  in  them  more  clearly  and 
certainly  its  validity  or  invalidity,  than  when  expressed  in  these  pro- 

7  Hamilton's  Logic,  p.  308. 


154  OF    REASONINGS. 

lix  scholastic  forms.  The  answer  we  would  prefer  to  give  is  as  fol- 
lows: Logic  is  a  science.  The  system  of  reduction  serves  the  pur- 
pose of  showing  that  all  reasoning  is  governed  by  the  same  principle, 
that  these  processes  of  thought,  whatever  shapes  they  may  take  natu- 
rally and  spontaneously,  are  in  all  cases  fundamentally  one  and  the 
same.  We  are  thus  enabled  to  comprehend  in  a  single  grasp  move- 
ments of  intellect  which  otherwise  would  seem  multifarious  and  per- 
plexed. We  attain  that  clear  unity  which  is  the  end  of  all  science. 
Our  practice  is  improved  by  such  investigation,  but  its  direct  object  is 
not  skill,  it  is  knowledge. 

§  6.  In  the  mnemonic  hexameters,  moods  of  the  same  figure  occur 
together.  We  present  on  the  opposite  page  a  scheme  in  which  the 
equivalent  moods  are  arranged  together.  Equivalent  moods  are  those 
reducible  to  each  other.  Their  names  have  the  same  initial  letter. 
The  three  methods  of  notation  are  also  exhibited.  This  scheme  brings 
to  light  several  important  facts,  among  others  the  following : 

Equivalent  moods  are  not  merely  reducible  to  the  same  mood  of 
Fig.  1,  but  are  reducible  to  each  other.  That  is,  a  syllogism  in  any 
mood  may  by  reduction  be  expressed  in  any  of  its  equivalents.  This 
is  evinced  by  the  symbolic  notation  being  similar  for  all  equivalents. 
But  a  syllogism  cannot  be  reduced  to  another  mood  not  equivalent. 
Thus  it  appears  that  the  variation  by  figure,  as  well  as  the  order  of 
premises,  is  in  a  sense  unessential,  accidental,  external ;  whereas  the 
variation  by  mood,  which  depends  on  the  quantity  and  quality  of  the 
premises,  is  essential  and  internal.  Hence  it  would  seem  to  be  logi- 
cally more  accurate  to  consider  the  syllogism  as  containing  under  it 
moods,  the  equivalents  being  the  species,  under  which  we  find  varie- 
ties in  figure,  and  then  we  reach  the  individual  moods  which  have 
received  proper  names.  A  subspecies  also  might  be  formed  of  those 
equivalent  moods  requiring  only  simple  conversion  in  order  to  reduc- 
tion. Such  are  absolutely  equivalent,  and  appear  in  each  of  the  four 
figures.  They  constitute  groups  in  the  scheme. 

Moods  which  have  the  same  initial  letter,  that  is,  equivalent  moods, 
conclude  the  same  formal  judgment.  Moods  in  B  conclude  A ;  those 
in  C  conclude  E;  those  in  D  conclude  I;  those  in  F  conclude  O. 
The  exceptions  are  Bramantip  and  Dokamok. 

The  linear  and  circular  notation  are  symbolic.  A  different  circular 
diagram  may  be  made  for  each  individual  mood,  the  relative  positions 
of  the  circles  being  varied  so  as  in  most  cases  to  express  the  individual 


FIGURE    AND    MOOD. 


155 


SYNOPSIS  OF  EQUIVALENT  MOODS. 

Equiv.  Moods.  IIs-  Graphic  N.  H"  Linear  N.  Eu«-  Circular  N. 

Fig.  1.  Barbara  C,  ^-:M,^-:F 

"    4.  Bramantip 


Fig.  1.  Celarent 
"    2.  Cesare 
"    2.  Camestres 
"    4.  Camenes 


(Rejected) 


"    3.  Disarais 
"    3.  Datisi 
"    4.  Dimavis 

"    3.  Dokamok 

(Bocardo) 


CRejected) 


Fig.  1.  Ferio 
"    2.  Festino 
"    3.  Ferison 
"    4.  Fresison 

"    2.  Fakofo 

(Baroco) 


;H-;M,^,r 
:^-:M,  — ,F 

(Rejected)     j 


1    3.  Darapti  C,  —  :M:  — ,r  M 


Ditto 


"    3.  Felapton  C:H*:M:«~,1 

"    4.  Fesapo  (Rejected) 


o   $  ®r) 


156  OF    REASONINGS. 

differences.  Tins,  however,  presents  no  advantages.  The  linear  nota- 
tion, which  is  not  thus  variable,  is  on  this  account  rather  to  be  pre- 
ferred. The  graphic  notation  is  not  symbolic,  but  consists  of  arbi- 
trary signs.  It  expresses  all  the  accidental  variations  in  external  form, 
whereas  the  linear  expresses  only  the  internal,  essential  feature,  i.  e., 
the  mood.  The  graphic,  used  in  the  scheme  to  express  extension, 
may  express  also  intension.  In  extension  the  copula  points  to  the 
predicate,  in  intension  to  the  subject ;  in  general,  the  copula  of  the 
conclusion  always  points  to  the  major  term.  In  comparing  the  sev- 
eral notations,  we  must  not  forget,  especially  in  case  of  moods  contain- 
ing m,  that  C  and  F  are  indifferent,  and  therefore  interchangeable. 

Arnauld,  after  detailing  what  Hamilton  calls  "  the  disgusting  rules 
for  reduction,"  pronounces  them  superfluous,  and  proposes  to  super- 
sede them  by  one  General  Rule  for  Reduction,  as  follows :  If  the 
terms  of  the  syllogism  do  not  appear  in  the  order  required  by  the 
first  figure,  make  them  assume  this  order  by  any  legitimate  conver- 
sion, also  transposing,  if  need  be,  the  premises. 

§  7.  We  are  now  prepared  to  examine  the  Fourth  Figure.  Its  le- 
gitimacy has  been  disputed  by  many  logicians.  Feeling  it  to  be  awk- 
ward, they  reject  it  as  an  encumbrance,  assigning  various  reasons. 
Hamilton  hotly  denounces  it  as  "  a  monster  undeserving  of  toleration, 
far  less  of  countenance  and  favor." 8  He  argues  that  it  is  unnatural 
and  useless,  because  the  premises  are  in  intension  while  the  conclusion 
is  in  extension,  and  that  passing  from  one  of  these  quantities  to  the 
other  in  the  same  syllogism  is  violative  of  the  order  of  thought,  and 
to  no  purpose.  To  this  we  object,  first,  that  his  assumption  that  the 
premises  are  in  intension  is  grounded  solely  upon  their  order,  which, 
we  repeat,  is  arbitrary,  and  hence  indicates  nothing  inherent  in  the 
reasoning.  We  object,  secondly,  that  such  alternations  of  quantity 
occur  very  frequently  in  the  other  figures,  are  often  to  good  purpose, 
and  in  some  cases  seem  essential  (i,  §  3).  If  so,  we  may  grant  they 
occur  in  Fig.  4,  without  furnishing  a  ground  for  rejecting  it.  Indeed, 
as  has  been  said,  these  quantities  cannot  stand  apart.  Every  logical 
judgment,  every  reasoning  is  in  both  at  once,  and  their  alternate 
predominance  is  not,  in  any  important  sense,  a  change  of  thought. 

Other  logicians  have  thought  so  well  of  Fig.  4  that  it  has  with- 
stood these  attacks  and  taken  deep  root  in  the  literature  of  Logic, 

8  Logic,  p.  303. 


FIGURE    AND    MOOD.  157 

so  that  every  elementary  treatise  must  give  it  place.  Yet,  truly,  if  it 
could  be  discarded  without  marring  the  symmetry  of  the  science, 
without  the  loss  of  any  essential  doctrine  or  form,  this  would  be-  a 
great  stride  towards  simplicity.  And  it  would  seem  not  difficult  to 
decide  the  question.  The  chief  reason  given  for  retaining  it  is  that 
Figure  requires  this  fourth  variation  to  exhaust  the  possible  forms; 
that  Fig.  4  is  essential  to  completeness,  however  rarely  used  or  awk- 
ward. But  this  is  true  only  if  the  order  of  the  premises  is  essential. 
We  have  decided  that  the  order  is  not  essential,  being  merely  conven- 
tional. It  follows  that  the  first  three  figures  exhaust  the  forms ;  and 
that  the  fourth  is  the  first  with  transposed  premises,  contrary  to  agree- 
ment, and  hence  ought  not  to  appear. 

The  advocates  of  Fig.  4,  however,  point  to  its  conclusion,  which  is 
not  that  which  Fig.  1  should  give,  and  claim  that  it  implies  an  essen- 
tial difference.  The  reply  is  not  difficult.  Let  us  consider  the  form 

S  is  M; 

M  is  P; 

.'.  P  is  S. 

Here  we  readily  see  that  the  conclusion  is  not  the  one  which  the  mind 
is  naturally  disposed  to  draw.  It  strongly  inclines  to  conclude  "  S  is 
P ;"  and  in  concluding  "  P  is  S,"  it  is  fully  conscious  of  a  revulsion. 
This  it  is  that  seems  so  awkward,  and  violative  of  that  directness 
which  should  characterize  the  simple  syllogism.  The  explanation  is 
that  the  reasoner  does  mentally  draw  the  conclusion  "  S  is  P,"  and  so 
reasons  in  Fig.  1 ;  and  then  immediately  infers  by  conversion  that  "  P 
is  S."  This  is  done  tacitly,  and  almost  unconsciously.  But  a  slight 
reflection  on  the  process  leaves  little  doubt  that  the  judgment "  S  is 
P"is  mentally  interpolated  between  the  premises  and  the  expressed 
conclusion.  A  concrete  example  will  perhaps  make  this  more  clear. 

Bram-     All  kings  are  men ; 

a-         All  men  are  mortals ; 

Direct —    (a-    .*.  All  kings  are  mortals  ;) — tacit  interpolation. 
Indirect— n tip.  .'.  Some  mortals  are  kings— by  conversion  per  accidem. 

Camencs  and  Dimaris  are  entirely  similar,  the  transposition  of  the 
premises  and  the  simple  conversion  of  the  conclusion  being  all  that  is 
requisite  to  present  them  as  Celarent  and  Darii.  May  we  not  rather 
say,  they  are  Celarent  and  Darii  (the  order  of  the  premises  being  non- 
essential)  with  the  conclusion  simply  converted. 


158  OF    REASONINGS. 

Fesapo  and  Fresison  are  each  reduced  to  Ferio  by  converting  both 
premises,  leaving  the  conclusion  intact.  This  reduction  does  not  re- 
quire the  transposition  of  the  premises.  It  is  not  probable,  however, 
that  the  mind  tacitly  performs  this  double  conversion  when  reasoning 
in  these  moods.  It  would  rather  seem  that  this- 'process  is  similar  to 
the  above.  Let  us  illustrate : 

Fes-     No  ghosts  are  angels; 
ap-      All  angels  are  spirits ; 

Direct—  (e-  .*.  No  ghosts  are  spirits ;) — tacit  interpolation. 
Indirect —  o.   .'.  Some  spirits  are  not  ghosts — by  conversion  per  accidens. 

This  interpolated  conclusion-  is  an  illicit  process  of  the  major  term. 
But  this  the  mind  feels,  and  instantly  restores  the  given  quantity  by 
converting  per  accidens.  The  case  with  Fresison  is  precisely  the  same. 
These  two  moods,  then,  are  illegitimate. 

We  are  therefore  justified  in  concluding  that  the  three  legitimate 
moods  of  Fig.  4  are  in  reality  those  of  Fig.  1  stated  irregularly  with 
transposed  premises,  and  having  an  indirect  conclusion  which  is  an 
immediate  inference  from  the  actual  and  direct  conclusion.  The  two 
'^Illegitimate  moods  are,  of  course,  to  be  condemned.  Consequently 
Fig.  4,  with  all  its  moods,  should  be  rejected  from  its  usurped  place 
in  the  logical  system,  and  its  legitimate  forms  should  be  classed  with 
the  irregular  forms  of  the  syllogism. 

The  fourth  figure  is  not  recognized  by  Aristotle,  nor  by  any  of  his 
early  followers.  Averroes,  in  his  Commentary  on  the  Organon,  at- 
tributes its  introduction  into  Logic  to  Galen,  who  flourished  a  thou- 
sand years  previously.  But  a  critical  examination  of  the  extant  logi- 
cal writings  of  the  physician  discovers  no  trace  of  it.  The  Spanish 
Moor  is  therefore  believed  to  have  been  mistaken.  As  it  does  not 
appear  in  any  extant  treatise  of  earlier  date  than  the  Commentary,  its 
origin  is  altogether  uncertain.  We  may  confidently  conclude,  however, 
that  it  did  not  originate  in  ancient,  but  in  early  mediaeval,  times. 

§  8.  In  concluding  this  discussion  of  the  simple  Aristotelic  syllo- 
gism, we  will  consider  a  charge  that  has  been  standing  against  it  ever 
since  the  days  of  Sextus  Empiricus,  back  to  whom  it  may  be  traced. 
It  alleges  that  the  conclusion  is  already  contained  in  one  or  both  prem- 
ises ;  that  what  is  to  be  proved  is  therein  assumed  to  be  true ;  that 
the  question  is  begged,  and  hence  that  by  means  of  the  syllogism  we 
can  make  no  real  progress  in  knowledge.  Thus  it  imputes  uselessness 
and  frivolity  to  the  whole  syllogistic  theory,  and  pronounces  its  pre- 


FIGURE    AND    MOOD. 

tensions  a  sham.  On  this  ground  Stewart,  Campbell,  and  a  number 
of  other  thinkers  have  rejected  Logic  with  some  display  of  scorn. 
The  charge  is  well  and  strongly  stated  by  Mill  thus : 

"  It  is  universally  allowed  that  a  syllogism  is  vicious  if  there  be 
anything  more  in  the  conclusion  than  was  assumed  in  the  premises. 
But  this  is,  in  fact,  to  say  that  nothing  ever  was  or  can  be  proved  by 
syllogism  which  was  not  known,  or  assumed  to  be  known,  before.  It 
must  be  granted  that  in  every  syllogism,  considered  as  an  argument 
to  prove  the  conclusion,  there  is  & petitio  principii.  When  we  say, 

All  men  are  mortal ; 
Plato  is  a  man ; 
.'.  Plato  is  mortal, 

it  is  unanswerably  urged  by  the  adversaries  of  the  syllogistic  theory 
that  the  proposition  '  Plato  is  mortal '  is  presupposed  in  the  more 
general  assumption  'All  men  are  mortal.'  In  short,  no  reasoning 
from  generals  to  particulars  can,  as  such,  prove  anything;  since  from 
a  general  principle  we  cannot  infer  any  particulars  but  those  which 
the  principle  itself  assumes  as  known.  This  doctrine  appears  to  me 
irrefragable."  9 

He  says  elsewhere,  "  From  this  difficulty  there  appears  to  be  but 
one  issue.  Its  refutation  seems  impossible  on  any  theory  which  con- 
siders the  syllogism  as  a  process  of  inference."  This  only  issue  he 
expounds  to  be  through  his  peculiar  theory,  which  denies  that  the  syl- 
logism is  an  inference  or  proof,  and  views  it  as  "  the  mere  interpreta- 
tion of  the  record  of  a  previous  process ;  the  major  premise  as  simply 
a  formula  for  making  particular  inferences ;  and  the  conclusion  as, 
not  an  inference  from  the  formula,  but  an  inference  drawn  according 
to  the  formula."  10  As  we  have  not  adopted  Mill's  theory  of  ratiocina- 
tion, we  need  not  state  his  reply  to  the  objection  which  seems  to  him 
irrefragable.  We  therefore  remain  in  the  toils  of  this  entanglement, 
and  must  make  our  exit,  if  possible,  by  other  means.11 


9  Logic,  p.  139.  10  Examination  of  Hamilton,  vol.  ii,  p.  235. 

11  Mansel  discusses  the  question  ably  in  the  Appendix  to  his  edition  of  Aldrich, 
Note  E.  He  directs  his  argument  chiefly  against  Mill,  showing  in  an  argumentum 
ad  hominem  his  inconsistency  in  these  statements  with  his  own  logical  principles. 
De  Morgan  examines  the  question  briefly  but  skilfully  under  the  head  of  "Falla- 
cies of  Petitio  Principii,"  Formal  Logic,  pp.  257-59.  Bain  endorses  and  follows 
Mill's  views, — Logic,  p.  208  sq.  Sec  also  Whately's  chapter  "  On  the  Discovery 
of  Truth,"  Logic,  p.  262  sq. 


100  OF    REASONINGS. 

Will  Hamilton  help  us?  In  speaking  of  the  usual  order  of  the 
propositions  in  the  formal  syllogism,  which  he  calls  "the  synthetic 
order,"  he  says,  "  On  this  order  the  objection  of  petitio  principii 
stands  hitherto  unrefuted,  if  not  unrefutable,  against  Logic."  ia  He  en- 
tertains the  odd  fancy  that  the  objection  can  be  got  rid  of  by  merely 
writing  the  propositions  in  a  different  order,  putting  the  conclusion 
first.  This  he  calls  "  the  analytic  order,"  and  insists  that  it  is  the  true 
order  in  thought  This  seems  much  like  a  solemn  joke.  Could  he 
really  think  that  the  difficulty  might  be  obviated  by  a  juggling  with 
an  order  of  words?  Truly,  if  a  speaker  starts  with  stating  his  conclu- 
sion, he  cannot  be  said  to  have  already  admitted  it  in  words.  But 
has  he  not  already  thought  it  in  a  premise  not  yet  expressed  ?  Else 
how  can  his  conclusion  be  a  conclusion  ?  Bo  wen,  not  seeing  the  joke, 
adopts  and  expands  this  reply  of  Hamilton  as  a  serious  and  sufficient 
reply  to  the  "  unrefuted  if  not  unrefutable"  objection.18 

We  must  help  ourselves  in  this  matter  as  well  as  we  can.  All  lo- 
gicians freely  admit  that  there  can  be  nothing  in  a  valid  conclusion 
that  is  not  contained  in  the  premises,  i.  e.,  in  both  premises,  both 
taken  together.  The  conclusion  of  a  syllogism  consists  merely  of  a 
succinct  and  explicit  statement  of  the  relation  of  two  notions,  which 
relation  is  thought  in  their  comparison  in  the  premises  through  a 
third  notion.  It  is  universally  allowed  after  Aristotle  that  a  medi- 
ate reasoning  is  not  three  successive  judgments  as  appears  when 
written  out  to  the  eye,  but  that  it  is  a  single  act  of  mind,  a  single 
judgment.  Hence  to  admit  that  the  premises  contain  the  conclu- 
sion is  pretty  much  the  same  thing  as  to  admit  that  the  conclusion 
contains  itself.  But  to  say  that  it  is  contained  already,  i.  e.,  previous- 
ly, in  the  premises  is  to  mistake  the  nature  of  a  reasoning.  The 
premises  as  premises  arc  logical,  but  not  chronological,  antecedents. 

Now  if  the  comparison  be  only  apparently  and  not  really  mediate, 
if  that  which  stands  for  the  middle  term  is  in  fact  identical  with  one 
of  the  extremes,  it  is  evident  that  we  have  but  two  terms,  and  the  con- 
clusion is  merely  a  repetition  of  this  known  relation.  This  is  fallacy. 
This  is  to  "  beg  the  question."  Herein  is  no  progress.  But  if  the 
medium  be  distinct  and  really  that  through  which  the  relation  of  the 
other  two  notions  is  ascertained,  then  this  is  not  to  "  beg  the  ques- 
tion," and  there  is  progress. 

12  Appendix  to  Logic,  p,  G23,    See  also  Discussions,  p.  004  (Am.  ed.). 

13  Logic,  p.  228  sq. 


FIGURE    AND    MOOD.  161 

Let  us  remember  that  the  premises  and  conclusion  are  correlatives, 
that  neither  can  exist  without  the  other.  It  is  a  very  common  case 
that  a  mind  may  be  in  full  and  familiar  possession  of  two  truths,  but, 
never  having  thought  them  together,  the  consequence  has  never  been 
thought,  and  is  to  this  mind  utterly  unknown.  It  may  have  occurred 
as  a  question  (qucesitum) ;  but  these  two  familiar  propositions,  which 
together  necessitate  it,  not  having  been  brought  together,  are  not  prem- 
ises, and  the  qucesitum  is  not  a  conclusion.  For  example,  everybody 
knows  that  young  infants  cannot  talk,  have  no  words,  nor  signs  of 
thoughts  that  are  not  merely  instinctive  effects.  Again,  no  one  doubts 
that  such  infants  really  think.  Yet  many  persons  have  never  brought 
these  truths  together  as  premises  of  a  conclusion.  They  may  have 
questioned  in  their  own  minds  the  fact  that  can  be  inferred,  but,  be- 
ing apart  from  these  truths,  it  was  a  question  merely.  But  bring  the 
truths  together  thus : 

Infants  have  no  language ; 
But  infants  reason ; 

and  is  it  not  instantly  seen  that  there  is  involved  in  this  statement  a 
new  truth  which  we  may  explicate  and  state  apart,  thus : 
.'.  Some  reasoning  can  be  done  without  language. 

Will  any  one  say  that  nothing  is  proved  here  ?  Is  there  not  a  step 
forward  in  knowledge,  an  advance  from  the  known  to  the  unknown  ? 
Many  persons,  in  view  of  this  simple  syllogism,  would  say,  Why,  of 
course,  I  might  have  known  that,  but  I  never  thought  of  it.  The  two 
premises  together  contain  the  conclusion,  but  this  is  not  to  "  beg  the 
question ;"  they  do  not  assume  it,  they  produce  it,  a  new  truth  dis- 
tinct from  either  alone. 

But  it  is  said  in  one  form  of  the  indictment  that  the  conclusion  is 
contained  in  one  of  the  premises  alone,  and  that  in  stating  it  we 
merely  repeat  what  is  already  said  in  this  proposition  apart,  as  in  the 
example  quoted  above  from  Mill.  The  objection  in  this  form  has 
been  greatly  confirmed  by  the  view  that  Arnauld  takes  of  the  syllo- 
gism. He  says  that  every  valid  syllogism  is  governed  exclusively  by 
this  principle :  "  One  of  the  two  antecedents  must  contain  the  conclu- 
sion, and  the  other  show  that  it  contains  it."  u  This  is  very  true,  and 
a  very  ingenious  and  excellent  view  of  the  syllogism  in  the  sense  in 
which  Arnauld  intends  the  statement.  But  it  is  not,  as  .is  claimed,  an 

14  Port-Royal  Logic,  pt.  iii,  chs.  x,  xi. 
11 


162  OF    REASONINGS. 

acknowledgment  of  petitio  principii,  nor  can  it  be  fairly  construed  to 
sustain  the  charge.  The  conclusion  is  contained  in  the  premise  in 
the  same  sense  that  any  single  notion  is  contained  under  one  broader, 
its  genus;  but  observe  that  the  other  premise  is  necessary  to  show 
this.  I  may  have  a  good  clear  conception  of  a  general  rule,  which  on 
sufficient  grounds  I  have  accepted  as  universally  true,  but  know  noth- 
ing whatever  of  a  multitude  of  cases  to  which  it  is  applicable.  We 
may  say  that  the  rule  contains  or  includes  these  unknown  cases,  but  I 
am  not  conscious  of  that  until  it  is  made  to  appear  by  bringing  them 
in  as  minor  premises,  and  then  I  progress  in  knowledge. 

For  illustration,  when  we  say  "  All  men  are  mortal,"  have  we  not 
already  virtually  said,  by  implication  at  least,  "Plato  is  mortal."  Not 
unless  we  have  also  said,  or  know,  or  thought  that  "  Plato  is  a  man," 
which  is  the  minor  premise.  " Plato"  may  be  a  statue,  or  a  book,  or 
a  town,  or  what  not.  I  must  first  think  that  "  Plato  is  a  man  "  before, 
under  this.  rule.  I  can  say  he  is  mortal.  The  bald  truisms  usual,  for 
simplicity's  sake,  in  logical  examples  lend  countenance  to  the  objection 
through  the  unwitting  mental  supply  of  the  obvious  minor  premise. 
'Yet  a  reasoning  very  similar  to  our  excmplum  was  found  needful  by 
Paul  and  Barnabas  at  Lystra.15  The  people  there  knew  very  well 
the  major  premise,  "No  man  should  be  worshipped."  St.  Paul  sup- 
plied the  needed  minor,  "  We  also  are  men,  of  like  passions  with  you ;" 
and  the  conclusion  contained  in  these  two  premises  was  so  obvious  that 
it  was  left  unexpressed.  But  let  us  take  a  case  in  which  each  premise 
is  questionable : 

No  murderer  hath  eternal  life ; 

All  warriors  are  murderers ; 
.'.  No  warrior  hath  eternal  life. 

Here  we  have  a  major  premise  which  some  persons  would  deny,  while 
admitting  the  minor;  and  many  who  would  admit  it  would  deny  the 
minor.  Hence,  in  the  estimation  of  either  class  one  of  these  premises 
may  be  affirmed  without  involving  the  affirmation  of  the  conclusion. 

Whately  says  that  the  object  of  reasoning  is  "  merely  to  expand 
and  unfold  the  assertions  wrapped  up,  as  it  were,  and  implied  in  those 
with  which  we  set  out."  Elsewhere  he  speaks  of  geometry  as  being 
all  wrapped  up  in  its  definitions  and  axioms.  I  suppose  this  is  tanta- 
mount to  the  statement  that  the  conclusion  is  virtually  contained  in 
the  premises.  I  do  not  object  to  Whately's  metaphor,  but  say  that 

15  Acts  xiv. 


FIGURE    AND    MOOD.  103 

knowledge  thus  wrapped  up  is  merely  virtual  or  potential,  and  to  be- 
come actual  knowledge  its  wrapping  must  be  unwrapped.  But  is 
virtual  or  potential  knowledge,  knowledge  at  all?  Is  not  real  knowl- 
edge only  that  which  is  actual  ?  Can  it,  indeed,  be  said  to  exist  when 
not  present  in  mind  ?  Only  in  that  very  shadowy  and  questionable 
shape  in  which  potential  energy  is  said  by  the  physicist  to  exist 
stored  up  in  an  inert,  inactive  mass.  A  keg  of  powder  contains  in  it 
an  explosion,  i.  e.,  potentially,  but  a  spark  is  needed  to  realize  it.  So, 
if  the  major  premise  contains  the  conclusion,  it  certainly  needs  the 
minor  to  bring  it  about.  A  boulder  on  a  mountain-top  has  stored 
up  in  it  an  immense  quantity  of  potential  energy.  But  it  stays  there 
very  ineffectively  until  some  minor  starts  it  rolling  down  the  steep, 
and  this  is  necessary  before  we  can  have  any  experience  of  its  force. 

Very  often,  in  our  search  after  truth,  a  question  clearly  arises  to 
establish  which  we  have  at  hand  the  major  premise,  but,  lacking  the 
minor,  we  are  utterly  unable  to  reach  a  conclusion.  Why  is  this  if  in 
affirming  the  major  we  have  already  affirmed  the  conclusion?  Why 
not  explicate  it,  and  state  it  as  established  ?  For  instance,  an  astrono- 
mer observes  a  new  comet,  and  at  once  asks  whether  it  will  return 
again  to  our  system.  He  knows  full  well  that  a  celestial  body  mov- 
ing in  a  hyperbolic  orbit  will  not  return ;  but  from  this  major  alone 
he  can  conclude  nothing  respecting  the  one  in  question.  He  labori- 
ously and  patiently  sets  to  work  to  establish  a  minor.  With  minute 
pains  he  determines  three  or  four  points  in  the  comet's  orbit,  and 
finally  is  enabled  to  affirm  that  its  orbit  is  hyperbolic.  Then,  but  not 
till  then,  the  question  resolves  into  the  now  established  conclusion 
that  this  comet  will  not  return.  A  large  part  of  our  thoughtful  in- 
vestigations is  a  search  after,  or  rather  an  effort  to  establish,  proposi- 
tions to  serve  as  minor  premises  under  familiar  general  rules,  in  order 
to  deduce  thereby  new  truth. 

Is  it  not  progress  in  knowledge  for  one  to  deduce  the  consequences 
of  new  facts  and  laws  obtained  by  observation  and  induction  ?  Is  not 
movement  from  the  obscure  and  confused  to  the  clear  and  distinct  an 
advance,  an  addition  ?  Is  not  a  discovery  of  the  true  relations  of  our 
intuitive  ideas  and  their  systematic  arrangement  something  gained, 
something  new  ?  All  this  is  accomplished  by  deductive  inference, 
and  by  it  alone.  The  objection  to  the  syllogism  reaches  too  far  to  be 
sound.  Were  it  so,  then  Euclid  and  Newton  labored  in  vain. 

Let  us,  finally,  glance  at  the  form  of  the  argument  that  assails  the 
syllogism.  The  eagle  of  the  Libyan  fable  was  slain  by  an  arrow 


164  OF    REASONINGS. 

feathered  from  its  own  wing.  So  the  armory  of  the  logician  has 
been  imagined  to  contain  the  fatal  weapon  of  its  own  destruction. 
The  empiricist  has  seized  the  syllogism,  but,  sheathing  his  own  sword, 
he  tries,  like  Giant  Despair,  to  get  his  captive  to  commit  suicide. 
Plainly  he  uses  the  syllogism  to  prove  the  syllogism  useless.  His 
argument  is  as  follows : 

Any  reasoning  that  proceeds  upon  the  assumption  of  its  conclusion  is  petit io 

principii; 

'•     The  Aristotelic  syllogism,  as  is  admitted  by  all  logicians,  proceeds  thus  ; 
V.  The  Aristotelic  syllogism  is  confessedly  petitio  principii. 

Surely  this  is  seething  the  kid  in  its  mother's  milk.  But  if  it  has 
proved  its  conclusion  true,  then  this  syllogism  is  itself  a  false  reason- 
ing, and  therefore  has  not  proved  its  conclusion  true.  A  self-contra- 
diction may  well  be  dismissed.  We  remark,  however,  that,  granting 
this  reasoning  to  be  sound,  still  the  syllogism  does  not  commit  suicide, 
for  the  minor  premise  is  false.16 

At  risk  of  being  prolix,  we  must  notice  another  phase  of  the  objec- 
tion which  Mill  confuses  with  the  above.  It  is  said,  very  ingeniously, 
that  quite  often  the  conclusion,  so  far  from  being  deduced  from  the 
premise,  is  actually  required  to  deduce  the  premise  itself.  Thus  we 
do  not  know  from  "  All  men  are  mortal "  that  "  Plato  is  mortal,"  but 
we  must  first  know  that  "  Plato  is  mortal "  in  order  to  know  that  it  is 
really  true  that  "  All  men  are  mortal."  The  objection  here  falsely  as- 
sumes that  to  attain  a  universal  proposition  we  must  first  know  all 
the  individual  cases  it  includes.  If  this  were  true,  then  few,  very  few, 
universal  propositions  would  be  possible.  But  it  is  not  true.  We 
obtain  a  universal  proposition,  such  as  the  one  cited,  not  from  an  in- 
spection of  all  cases,  not  by  deduction,  but  by  an  induction  from  per- 
haps a  single  case,  or,  at  most,  from  a  very  limited  number.  Once  in 
possession  of  it,  we  proceed  to  bring  other  cases,  hitherto  unob- 
served, under  it,  and  thereby  draw  new  specific  conclusions. 


18  We  should  perhaps  note  that  the  usual  vague  and  inaccurate  sense  of  the 
phrase  petitio  principii  has  been  accepted  in  this  reply.  Its  proper  meaning  will 
be  examined  hereafter. 


FIGURE    AND    MOOD.  1C5 

§  9.  Praxis.  Supply  the  conclusion  to  each  of  the  following  pairs 
of  premises.  Prefix  to  each  syllogism  the  name  of  its  mood  (§  5). 
If  not  in  Fig.  1,  reduce  it  thereto.  To  Baroco  and  Bocardo  apply 
also  the  test  per  impossibile.  The  regular  order  of  the  propositions 
is  preserved  throughout  this  section,  the  major  premise,  the  one  con- 
taining the  predicate  of  the  conclusion  viewed  in  extension,  being 
stated  first. 

1.  Whoever  possesses  prudence  possesses  all  virtue; 

Whoever  possesses  one  virtue  must  possess  prudence. — Aristotle. 

2.  Prudence  has  for  its  object  the  benefit  of  individuals ; 
But  prudence  is  a  virtue. 

3.  No  good  action  results  in  evil ; 
Some  alms-giving  results  in  evil. 

4.  All  abstract  studies  strengthen  the  intellect ; 
Exercises  that  strengthen  the  intellect  are  profitable. 

5.  No  science  is  capable  of  perfection ; 
All  science  is  worthy  of  culture. 

6.  No  vicious  conduct  is  praiseworthy ; 
All  heroic  conduct  is  praiseworthy. 

7.  All  pride  is  inconsistent  with  religion ; 
Some  pride  is  commended  by  the  world. 

8.  No  duty  involves  loss; 

To  give  freely  is  occasionally  a  duty. 

9.  All  true  philosophers  account  virtue  a  good  in  itself ; 

The  Epicureans  do  not  account  virtue  a  good  in  itself. — Cicero. 

10.  No  one  governed  by  passion  is  free ; 
Sensualists  are  governed  by  passion. 

11.  All  good  reasoners  are  candid; 
Some  infidels  are  not  candid. 

12.  True  poets  are  men  of  genius; 

Very  unwise  men  have  proved  true  poets. 

1 3.  No  virtue  is  a  natural  quality ; 

Every  natural  quality  has  God  for  its  author. 

14.  Some  kinds  of  anger  are  not  unrighteous; 
Every  kind  of  anger  is  a  passion. 

1 5.  Some  of  our  tax-laws  are  oppressive  measures ; 
All  oppressive  measures  should  be  repealed. 

1 6.  No  truth  is  worthless ;         • 
Many  truths  are  misapplied. 


166  OF    REASONINGS. 

17.  Some  of  the  truths  affecting  human  conduct  are  speculative; 
All  that  affects  human  conduct  is  important. 

18.  No  moral  principles  are  animal  impulses; 
Nearly  all  animal  impulses  are  principles  of  action. 

19.  All  expedient  acts  are  comformable  to  nature; 
Nothing  conformable  to  nature  is  hurtful  to  society. 

Supply,  in  the  following,  any  lacking  proposition.     Prefix  the  name 
of  its  mood.     Write  the  linear  and  graphic  notation  of  each. 

20.  All  planetary  bodies  move  in  elliptic  orbits ; 
Therefore  the  orbits  of  the  asteroids  are  elliptic. 

21.  An  inflated  currency  enables  many  persons  to  make  rapid  fortunes ; 

hence,  since  this  is  promotive  of  national  prosperity,  one  way 
to  promote  national  prosperity  is  to  inflate  the  currency. 

22.  He  that  is  always  anxious  is  never  happy;  but  covetous  men  are 

always  anxious. 

23.  Disgrace  is  never  an  infliction  of  nature;  therefore  natal  deform- 

ity is  no  disgrace. 

24.  He  that  spareth  the  rod  hateth  his  child ;  hence  no  loving  parent 

spares  the  rod. 

25.  Since  every  partisan  is  prejudiced,  and  no  prejudiced  person  can 

be  a  just  judge,  none  of  our  reliable  judges  are  partisans. 

26.  Whatever  purifies  the  heart  is  a  blessing ; 
But  there  are  afflictions  that  purify  the  heart. 

27.  Sometimes  very  bad  men  attain  high  public  honors;  but  bad  men 

are  always  truly  contemptible. 

28.  All  men  are  liable  to  sorrow ;  hence  some,  at  least,  of  those  who 

are  boasting  of  continuous  prosperity  may  come  to  grief. 

29.  There  are  practically  virtuous  men  who  are  necessitarians;  it  fol- 

lows that  while  all  necessitarians  speculatively  abolish  the  dis- 
tinction between  vice  and  virtue,  some  who  do  this  are  never- 
theless, in  practice,  virtuous. 

30.  The  connection  of  mind  with  matter  is  incomprehensible;  but 

being  most  certain,  there  are  things  very  credible  which  are 
beyond  our  comprehension. 

31.  Not  every  war  is  impolitic;  but  every  one  is  ruinous;  hence  a 

ruinous  procedure  is,  in  some  cases,  good  policy. 

32.  No  virtue  is  contrary  to  the  love  of  truth ;  but  there  is  a  love  of 

peace  which  is  opposed  to  a  love  of  truth. 


FIGURE    AND    MOOD.  167 

33.  Nothing  that  must  be  repented  of  is  desirable.     Now  many  of 

our  most  intense   enjoyments  constrain  repentance.     Few  of 
these,  then,  are  truly  desirable. 

34.  Prejudices  are  in  no  case  compatible  with  perfection ;  yet  some 

are  innocent. 

35.  A  fallacious  argument  is  not  a  legitimate  mode  of  persuasion ; 

A  legitimate  mode  of  persuasion  sometimes  fails  to  gain  acquies- 
cence ; 
.'.  Not  all  those  arguments  are  fallacious  that  fail. 

36.  Virtue  is  always  attended  by  discretion ;  but  there  is  a  zeal  with- 

out discretion. 

37.  No  truth  applicable  to  practice  should  be  neglected ;  but  any  one 

may  seem  not  to  be  practical ;  hence  some  seemingly  unprac- 
tical truths  should  not  be  neglected. 

38.  None  who  have  won  enduring  fame  have  ever  lacked  wisdom  or 

industry ; 
Those  failing  in  these  requisites  constitute  the  great  majority  of 

men; 
.*.  Few  attain. 

In  the  following  miscellaneous  reasonings  the  order  of  the  proposi- 
tions is  still  preserved,  but  the  several  propositions  themselves  are 
more  or  less  irregular,  and  some  are  omitted.  Bring  the  reasonings 
into  syllogistic  form,  and  prefix  the  name  of  its  mood  to  each.  If 
found  defective,  state  what  rule  is  violated. 

39.  Theft  is  a  crime;  yet  some  kinds  were  legal  at  Sparta. 

40.  Every  virtue  promotes  general  happiness ;  but  exclusive  self-cult- 

ure does  not ;  it  has  therefore  no  moral  worth. 

41.  There  is  no  growth  without  sunshine,  and  these  flowers,  being  de- 

prived of  it,  will  not  grow. 

42.  Who  would  offer  a  bribe  would  receive  a  bribe.     Now,  no  one 

who  would  receive  a  bribe  is  fit  for  public  office;   hence  no 
one  fit  for  office  buys  votes. 

43.  Whatever  is  universally  believed  must  be  true.     This  may  be  said 

of  the  existence  of  God,  which,  therefore,  must  be  a  truth. 

44.  Some  few  men  at  least  are  truly  honorable,  yet  all  have  imperfec- 

tions ;  hence  some  arc  so  who  have  imperfections. 

45.  The  truly  virtuous  are  the  truly  happy.     The  poor  are  often  the 

one,  and  therefore  the  other. 

46.  No  sin  is  excusable.     Some  faults  are,  and  are  therefore  not  sins. 


168  OF    REASONINGS. 

47.  Hard  study  strengthens  the  mind,  but  wearies  the  flesh ;  so  that 

what  wearies,  strengthens. 

48.  Every  candid  man  acknowledges  merit  in  a  rival ; 
Every  learned  man  does  not  do  so ; 

/.  Every  learned  man  is  not  candid. 

49.  It  is  characteristic  of  theft  to  get,  though  not  by  gift,  something 

for  nothing ;  this  gambling  does,  and  thus  is  akin  to  theft. 

50.  A  true  evolution  is  caused  wholly  from  within  ;  but  since  very  few 

beings,  if  any,  have   been   exempt  from   adventitious   causes, 
scarcely  any,  perhaps  none,  have  been  evolved. 

51.  Any  disregard  of  moral  order  is  wrong; 

Every  action  disregards  moral  order  whose  moral  quality  is  doubtful ; 
.'.  Any  action  doubtful  as  to  its  moral  quality  is  not  doubtful  as  to 
its  moral  quality. 

52.  All  do  not  strive,  but  all  wish  to  succeed ;  hence  not  all  strive 

who  wish  to  succeed. 

53.  What  is  not  in  Scripture  is  not  binding  on  conscience ; 

Since  many  ecclesiastical  canons  are  not  found  therein,  they  may 
be  disregarded. 

54.  Few  men  are  entirely  unworthy  of  respect ; 
Most  men  are  unlearned ; 

.*.  Some  unlearned  men  are  worthy  of  respect. 

55.  No  one  is  rich  who  is  not  content ; 
No  miser  is  content ; 

.*.  No  miser  is  rich. 

56.  Some  Congressmen  are  evidently  ignorant  of  political  economy ; 
Such  are  unfit  to  legislate ; 

Hence  some  persons  unfit  for  the  position  are  sent  to  Congress. 

57.  Flesh  and  blood  cannot  inherit  the  kingdom  of  God ; 
Its  heirs  are  human  beings ; 

.*.  Some  of  us  shall  not  retain  these  vile  bodies. 

58.  All  imprudent  acts  are  not  vicious ;  all  are,  however,  foolish ;  and 

so  folly  is  not  always  vice. 

59.  No  impenitent  sinner  can  hope  to  escape  the  wrath  of  God,  yet 

even  the  most  hardened  wish  to  escape ; 
Hence  not  all  who  desire  it  can  hope  for  salvation. 

60.  Scarcely  any  of  the  ship's  company  could  swim ; 
Yet  of  the  numerous  crew  only  a  few  perished ; 

.'.  Some  could  not  swim  who  nevertheless  survived. 

61.  Some  x  is  y  ;  every  y  is  not  z  ;  hence  some  x  is  not  z. 


FIGURE    AND    MOOD.  169 

62.  Bacon  was  a  notable  statesman ;  and  as  lie  was  a  great  philosopher, 

we  infer  that  great  philosophers  are  also  statesmen. 

63.  Whatever  is  of  practical  use  is  worthy  of  attentive  study ; 
Syllogistic  reduction  is  of  no  practical  use  ; 

.'.  Syllogistic  reduction  is  not  worthy  of  attention. 

64.  The  ancient  Greeks  produced  the  greatest  masterpieces  of  art ; 
The  Laceda3monians  were  ancient  Greeks ; 

.*.  They  produced  such  masterpieces. 

65.  All  prisoners  are  restrained  from  enjoying  the  common  right  of 

personal  liberty ; 

But  sailors  on  shipboard  are  not  prisoners ; 
.'.  They  enjoy  personal  liberty. 

66.  Whatever  causes  intoxication  should  be  prohibited ; 
The  use  of  wine  causes  intoxication ; 

/.  The  use  of  wine  should  be  prohibited. 

67.  No  sentient  being  is  without  a  nervous  system ; 
The  sensitive  mimosa  is  not  sentient ; 

.'.  The  sensitive  mimosa  has  no  nervous  system. 

68.  The  man  of  strong  will  conquers  his  passions,  and  so  does  he  that 

successfully  resists  temptation ; 
.*.  Whoever  does  not  yield  to  temptation  possesses  a  powerful  will. 

69.  All  rational  beings  are  accountable  for  their  actions ; 
But  many  that  suffer  punishment  are  irrational ; 

/.  Many  that  suffer  punishment  are  not  accountable  for  their  actions. 

70.  Suicide  is  simply  one  form  of  voluntary  death;  and  voluntary 

death,  in  some  form  or  other,  has  been  embraced  by  many  he- 
roes and  martyrs ;  so  suicide  is  not  always  to  be  condemned. 


170  OF    REASONINGS. 


III.  QUANTITATIYES. 

§  1.  The  quantitative  or  mathematical  judgment  has  already  been 
considered  at  some  length.  It  is  now  requisite  to  consider  specially 
reasonings  in  the  quantitative  whole.  Quantitative  judgments  are  very 
common.  We  sometimes  reason  with  them  alone,  and  in  other  rea- 
sonings they  intermingle  with  qualitative  judgments.  In  neither 
case  is  such  reasoning  governed  by  the  rules  of  the  Aristotelic  syllo- 
gism. The  old  Logic  does  not,  I  believe,  recognize  these  judgments 
nor  these  reasonings ;  certainly  not  as  distinct  in  kind,  and  governed 
by  special  laws.  It  would  require  all  to  be  reduced  to  the  Aristotelic 
syllogism,  and  brought  in  subjection  to  its  rules.  This  is  in  most, 
perhaps  in  all,  cases  possible,  but  requires  more  or  less  violence.  That 
is  to  say,  the  unity  thus  attained  is  not  the  result  of  analysis,  showing 
that  ultimately  these  kinds  of  reasoning  are  one  in  form  and  principle, 
but  is  attained  by  pressing  the  one  into  the  mould  of  the 'other,  and 
thus  forcing  it  into  an  unnatural  form.  But  the  object  of  Logic  be- 
ing to  exhibit  the  essential  nature  of  thought  in  its  original  forms, 
it  should  recognize  and  treat  these  judgments  or  reasonings  in  the 
quantitative  whole  apart  from  others,  and  assign  to  them  their  special 
laws.  Pure  Mathematics  proceeds  almost  exclusively  in  these  quanti- 
tative forms ;  and  the  anatomical  sciences,  which  are  all  essentially  sci- 
ences of  dissection  and  naming,  deal,  primarily  at  least,  with  quantities 
and  sections,  and  not  with  qualities  and  kinds.  Logic,  as  fundamen- 
tal to  all,  should  explain  these  processes,  exhibiting  the  native  manner 
of  thought  in  all  its  forms. 

When  equivalence  exists  between  two  individuals,  or  between  two 
aspects  or  thoughts  of  the  same  individual,  the  copula  means  "  is 
equal  to"  or  " is  the  same  as,"  and  may  be  expressed  by  the  mathe- 
matical sign  of  equality.  E.  g.,  "The  population  of  London  is  (  =  ) 
double  that  of  New  York ;"  "The  population  of  London  is  (=)  one 
million."  The  principle  governing  reasoning  with  such  propositions 
is  the  axiom  "  Things  that  are  equal  to  the  same  thing  are  equal  to 
each  other."  The  first  part  of  the  Canon  of  Replacement  (i,  §  4), 
"  Equivalent  notions  may  replace  each  other,"  will  be  found  to 
be  more  general  in  its  application,  and  hence  is  preferable  to  the 


QUANTITATIVES. 

axiom.  The  typical  form  of  this  syllogism  of  equivalence  is  the 
following : 

A  =  U; 

B  =  C; 

.'.  A  =  C. 

A  concrete  example  in  this  form  is  as  follows : 

The  density  of  the  human  body  is  the  density  of  water  ; 
The  density  of  water  is  the  density  of  air  taken  817  times ; 
.'.  The  density  of  the  human  body  is  817  times  the  density  of  air. 

It  will  be  observed  that  the  middle  term  here  is  a  standard  of  meas- 
ure. And  this  gives  occasion  to  remark  the  logical  function  of 
standards  of  measure  of  all  sorts.  They  furnish  the  media  through 
which  we  are  enabled  to  compare  quantities  which  cannot  be  immedi- 
ately compared.  The  yard,  the  bushel,  the  pound,  the  atomic  weight 
of  hydrogen,  the  thermometer,  barometer,  electrometer,  etc.,  supply 
us  with  middle  terms  through  which  to  reason  in  our  calculations. 

The  following  is  an  example  of  the  negative  syllogism  of  equiva- 
lence, the  only  formal  variation  of  which  it  is  susceptible : 

Selfishness  is  not  the  essence  of  virtue ; 
Duty  is  the  essence  of  virtue ; 
.*.  Duty  is  not  selfishness. 

We  remark  that  all  the  terms  in  this  particular  example  happen  to  be 
abstract.  In  general,  then,  abstract  notions  as  well  as  concrete  may 
be  thought  in  the  quantitative  whole. 

In  the  equivalent  syllogism,  the  order  of  premises  is  obviously  in- 
different. The  order  of  subject  and  predicate  is  also  indifferent. 
That  is,  either  term  may  be  made  the  subject  of  thought,  and  the 
other  the  predicate,  without  other  change.  The  distinction  of  major 
and  minor  terms,  and  consequently  that  of  major  and  minor  premises, 
does  not  exist,  the  terms  being  equivalent.  The  equivalent  proposi- 
tion -is  always  and  only  simply  convertible.  The  doctrine  of  Conver- 
sion, then,  has  no  place  relative  to  this  syllogism.  It  follows,  also,  that 
Figure  is  of  no  moment,  and  is  to  be  disregarded.  Moods  are  re- 
duced to  two,  the  positive  and  the  negative ;  for  the  quantification  of 
every  term  is  always  total.  Questions  concerning  distribution  and 
non-distribution  cannot,  then,  arise. 

These  eliminations  render  the  logical  treatment  of  this  syllogism 
exceedingly  simple.  Perhaps  from  this  simplicity  it  is,  as  well  as 
from  its  clear  intuitive  exactness,  that  elementary  mathematics  is 
within  the  grasp  of  immature  minds,  even  children  often  being  able 


172  OF    REASONINGS. 

to  apprehend  it  quite  thoroughly ;  whereas  reasoning  in  the  logical 
whole  with  the  Aristotelic  syllogism  as  the  unit  form  requires  more 
mental  discipline  and  maturity.  Hamilton  impetuously  declares  "math- 
ematics not  a  logical  exercise."  3  It  would  perhaps  be  wiser  to  hold 
with  Coleridge  that  "  Mathematics  is  no  substitute  for  Logic,"  and  to 
consider  mathematical  studies  as  the  proper  discipline  preparatory  to 
logical  studies." 

It  will  be  well  to  observe  that  the  distinction  taken  between  logical 
and  mathematical  reasoning  is  not  identical  with  the  familiar  distinc- 
tion between  moral  reasoning  and  demonstration.  Moral  reasoning, 
better  called  dialectics,  often  occurs  in  the  quantitative  whole,  and  is 
then  mathematical,  yet  it  always  involves  more  or  less  uncertainty. 
Demonstration  is  in  many  cases  not  quantitative  or  mathematical,  but 
always  carries  with  it  certainty.  The  difference  between  these  is  that 
any  dialectics  involves  to  some  extent  empirical  matter,  and  hence 
falls  short  of  certainty ;  whereas  demonstration  is  exclusively  from 
intuitive  principles,  and  carries  their  necessity  along  with  it.  This 
distinction,  then,  is  not  grounded  on  anything  peculiar  in  the  nature 
of  the  reasoning  employed,  which  in  all  cases  carries  with  it  just  the 
same  approximation  to  certainty  that  belongs  to  the  premises,  but  it 
is  found  in  the  nature  of  the  premises  themselves.  According  to  its 
definition  by  Aristotle,  demonstrative  reasoning,  producing  scientific 
knowledge  in  the  strictest  sense,  requires  a  conviction  of  the  certainty 
of  the  propositions  laid  down.3  His  scholastic  followers  devised  the 
following  syllogism  as  a  specimen  of  the  "  Demonstratio  potissima :" 

Omne  animal  rationale  est  risibile ; 
Omuis  homo  est  animal  rationale; 
ergo,  Omnis  homo  est  risibilis. 

Here  is  complete  identity  in  the  terms,  and  the  reasoning  may  be 
readily  construed  in  the  mathematical  whole ;  but  its  major  premise 
is  empirical,  not  intuitive,  not  a  priori,  and  hence  it  falls  short  of 
demonstration.  In  moral  reasoning  we  proceed  from  what  is  granted 

1  See  in  Discussions,  Education,  Article  1st, "  On  the  Study  of  Mathematics  as  an 
Exercise  of  Mind."     See  also  an  article  in  the  Athenaeum  for  Aug.  24th,  1850. 

2  The  distinction  drawn  between  mathematical  and  logical  reasoning  implies 
that  the  mathematical  is  not  logical.    The  latter  term,  unfortunately,  is  used  thus 
in  a  specific  sense.     In  its  general  sense  all  reasoning  is,  of  course,  logical. 

3  Anal.  Post,  i,  2,  1.     Aristotle  treats  of  demonstration  in  the  Posterior  Ana- 
lytics,  especially  in  chs.  i-xiii,  drawing  his  illustrations  from  pure  mathematics. 


QUANTITATIVES.  173 

by  the  disputant ;  the  principia  must  first  be  allowed.  In  demonstra- 
tive reasoning  there  is  no  concession ;  or  rather  there  can  be  no 
disputant.  Pure  mathematics,  which  is  strictly  demonstrative,  fur- 
nishes the  clearest  illustrations  of  quantitative  reasonings. 

§  2.  Let  us,  then,  turn  our  attention  to  pure  mathematics,  and  there- 
in to  synthetical  geometry,  to  observe  the  application  of  quantitative 
reasoning,  and  to  ascertain  how  truly  and  best  to  exhibit  its  logical 
process.  We  find  that  geometry  makes  some  use  of  qualitative  rea- 
soning, as  when  it  has  proved  of  triangles  in  general,  or  of  the  genus, 
that  the  three  angles  are  together  equal  to  two  right  angles,  it  after- 
wards applies  this  truth  to  the  several  species  of  triangle — the  equilat- 
eral, the  isosceles,  the  scalene.  We  find,  also,  that  it  sometimes  uses 
comparative  syllogisms,  but  that  by  far  the  greater  part  of  its  mediate 
inferences  are  in  equivalent  syllogisms. 

Geometry,  which  is  the  science  of  spatial  magnitudes,  supplies  itself 
at  the  outset  with  a  series  of  technical  terms  by  means  of  defini- 
tions analyzing  our  complex  notions  of  various  magnitudes.  It  then 
lays  down  certain  postulates  concerning  these.  Thirdly,  it  states  in- 
discriminately certain  axioms.  These  are,  however,  of  two  kinds: 
1st,  Certain  synthetical  judgments,  stating  the  self-evident  properties 
of  spatial  magnitudes,  such  as  "  Two  straight  lines  cannot  enclose 
a  space"  (Ax.  x) ;  and,  2d,  Certain  analytical  judgments,  such  as 
"Things  equal  to  the  same  are  equal  to  each  other"  (Ax.  i).  Accord- 
ing to  Kant,  the  first  are  geometrical  axioms  proper,  and  must  be  as- 
sumed as  intuitively  evident  before  any  of  the  more  complex  relations 
can  be  known  by  demonstration.  They  constitute  the  ultimate  prem- 
ises from  which  the  science  proceeds,  and  are,  therefore,  its  peculiar 
basis.  Those  of  the  second  class  express  general  conceptions  of  equal- 
ity and  inequality  relative  to  magnitudes.  They  are  derived  from  the 
Primary  Laws  of  Thought  as  applied  to  quantity,  and,  corresponding 
to  the  Canon  and  general  rules  of  the  qualitative  syllogism,  govern,  in 
a  mode  entirely  similar,  our  inferences  in  the  quantitative  whole.* 

It  has,  however,  been  usual  for  logicians  to  regard  these  analytical 

4  Axiom  1st  of  Euclid  (given  above)  is  the  Canon  of  mediate  inference.  Nos.  6 
and  7  are  merely  modified  statements  of  the  same.  The  other  analytic  axioms, 
Nos.  2  and  3,  4,  5,  which  are  deducible  from  it,  are  Canons  of  immediate  inference, 
corresponding  to  "complex  conceptions"  (Part  3d,  ii,  §  5).  E.  g.,  As  from  "A 
horse  is  an  animal,"  and  "Whatever  is  young  is  strong,"  we  immediately  infer 
"  A  young  horse  is  a  strong  animal,"  so  under  the  axiom  "  The  sums  of  equals 
are  equal,"  we  can  immediately  infer  from  a  =  6,  and  c  =  d,  that  a+c  =  b+d. 


174  OF    REASONINGS. 

axioms,  together  with  the  synthetical,  as  ultimate  premises  in  geome- 
try, and,  in  exhibiting  the  logical  analysis  of  a  demonstration,  to  place 
one  or  the  other  as  the  major  premise  of  nearly  every  syllogism.  E.  g. : 

Magnitudes  which  are  equal  to  the  same  are  equal  to  each  other ; 

Magnitudes  equal  to  the  adjacent  exterior  and  interior  angles  of  a  triangle  are 

equal  to  the  same  ; 
.'.  They  are  equal  to  each  other. 

Magnitudes  equal  to  the  adjacent  exterior  and  interior  angles  of  a  triangle  are 

equal  to  each  other ; 
The  three  interior  angles  and  two  right  angles  are  equal  to  the  adjacent  exterior 

and  interior  angles ; 
.'.  They  are  equal  to  each  other. 

All  this  is  very  true  and  formal,  but  very  prolix  and  operose.  Much 
in  this  way  Mill  exhibits  the  analysis  of  Euclid's  Proposition  v,  bk.  i;6 
and  a  similar  analysis  of  the  same  proposition  from  certain  old  scho- 
lastic logicians  may  be  found  in  Mansel's  Aldrich.0 

Now  it  is  very  possible  to  exhibit  an  analysis  of  arguments  in  the 
logical  whole  in  the  same  manner,  making  one  of  the  dicta  of  Aristotle 
the  major  premise  of  the  syllogism ;  but  both  process  and  result 
would  be  cumbersome  and  artificial.  It  is  far  simpler,  clearer,  and 
more  natural  to  treat  geometrical  reasonings  as  we  treat  qualitative 
reasonings.  Let  us  take  the  analytic  axioms  as  canons  governing 
the  form  and  authorizing  the  process,  and  develop  the  demonstration 
by  a  direct  chain  of  quantitative  syllogisms.  If  you  ask  me  to  jus- 
tify my  Canon,  I  do  it,  as  I  justify  Aristotle's  dicta,  by  deducing  it 
from  the  Primary  Laws.  .  The  above  syllogisms  would  then  reduce  to 
the  one  following : 

The  interior  angles  of  a  triangle  are  equal  to  an  adjacent  exterior  and  interior 

angle ; 

But  these  are  equal  to  two  right  angles ; 
.*.  The  interior  angles  are  equal  to  two  right  angles. 

The  expression  is  rendered  more  facile  by  the  use  of  a  lettered  figure, 
as  is  customary,  whereby  two  or  three  letters  take  the  place  of  a  verbal 
description  of  a  part.  This  method  of  exhibiting  the  logical  analy- 
sis of  a  geometrical  proof  is  not  only  far  simpler,  shorter,  and  more 
direct  than  the  usual  way,  but  it  seems  to  me  to  correctly  repre- 
sent the  actual  mental  process,  which  the  other  does  not. 

6  lagie,  pp.  162,  163.  °  Appendix,  Note  L. 


QU  ANTITATI VES.  1 7  5 

§  3.  "  This  simple  reasoning,"  says  Dr.  Reid,  "  cannot  be  brought 
into  any  syllogism  in  mood  and  figure : 

A  is  equal  to  B ; 

B  is  equal  to  C ; 

.'.  A  is  equal  to  C."  7 

And  hence  this  eminent  philosopher  rejected  Logic.  It  is  remarkable 
that  Bain  uses  the  following  language :  "  Logicians  are  aware  that  the 
form  'A  equals  B,  B  equals  C,  therefore  A  equals  C,'  is  not  reducible 
to  the  syllogism.  So  with  the  relation  of  'greater  than'  in  the  argu- 
ment a  fortiori.  Yet  to  the  ordinary  mind  these  inferences  are  as 
natural,  as  forcible,  and  as  prompt  as  the  syllogistic  inference." 8  He 
ought,  then,  to  follow  Dr.  Reid,  and  give  up  Logic.  Reid  means  to 
say  that,  taking  the  copula,  according  to  approved  logical  rule,  to  be 
"«s,"  and  all  that  follows  it  to  be  the  predicate,  we  have  in  this  rea- 
soning four  terms:  1st,  "A;"  2d,  "equal  to  B ;"  3d,  "B;"  4th, 
"  equal  to  C ;"  and  this  is  unavoidable,  so  that  this  simple  and  un- 
questionably good  inference  is,  according  to  the  rules  of  your  boasted 
Logic,  the  fallacy  of  Quaternio  terminorum  !  Away  with  it ! 

The  demand  is  to  construe  this  quantitative  reasoning  as  a  qualita- 
tive syllogism  subject  to  Aristotle's  Dictum  de  omni.*  A  and  B  are 
presumed  to  be  two  different  things.  But  how  much  of  A  is  here 
thought?  Only  one  mark,  its  quantity.  And  so  of  B.  Hence  the 
first  premise  becomes  "  The  quantity  of  A  is  equal  to  the  quantity  of 
B ;"  "  The  cost  of  the  museum  is  equal  to  the  university  debt ;"  i.  e., 
these  two  quantities  are  equal.  But  the  mere  quantity  of  a  thing  is 
a  pure  abstraction,  and  the  two  quantities,  taken  apart  from  all  other 
attributes,  are,  if  absolutely  equal,  indistinguishable  in  thought,  and 
therefore  are  to  us  the  same.  Hence  the  true  interpretation  of  the 
thought,  and  its  full  and  accurate  expression  is,  "  The  quantity  of  A 
is  the  quantity  of  B  ;"  "  The  amount  of  the  cost  of  the  museum  is 
(the  same  as)  the  amount  of  the  university  debt;"  $75,000  is  $75,000, 
indistinguishably.  A  mere  form  of  words  cannot  bind  Logic,  which 
postulates  to  interpret  and  express  the  thought.  Now,  with  our  prop- 
osition in  this  form,  no  difficulty  remains ;  for  we  may  transfer  to  the 
logical  whole,  taking  the  terms  as  coextensive,  and  yet  think  the  sub- 
ject as  contained  under  the  predicate.  Our  syllogism,  then,  is  Barbara. 
But  all  this  should  not  be  required.  The  phrase  "is  equal  to"  is 

7  See  Hamilton's  Reid,  p.  702.  B  Logic,  p.  183. 

B  The  treatment  of  this,  and  the  cases  discussed  in  the  next  section,  by  Mansel 
in  his  edition  of  Aldrich,  Appendix,  Note  D,  is  quite  unsatisfactory. 


OF    REASONINGS. 

properly  to  be  viewed  as  the  copula  interpreted.  The  same  demand 
might  be  made  to  bring  "  A  is  contained  under  B,"  or  "  A  is  a  kind 
or  species  of  B,"  or  "  A  has  for  one  of  its  marks  B,"  under  the  rule 
that  the  is  is  the  copula,  and  what  follows  is  the  predicate.  Then, 
upon  the  result,  the  demand  might  be  repeated,  and  so  ad  infinitum. 

So  far  of  quantitative  reasoning  in  the  equivalent  degree,  misnamed 
the  "  positive  "  degree. 

§  4.  Propositions  in  the  comparative  degree  have  for  their  copula 
"  is  greater  than,"  or  its  correlative,  "  is  less  than,"  for  which  the  math- 
ematical sign  of  inequality  may  be  substituted.  The  typical  form  of 

the  syllogism  is : 

A>B; 

B  >C; 

/.  A  >  C. 

Simply  converting  these  propositions,  we  invert  the  meaning  of  the 

copula  and  read : 

B  is  less  than  A ; 

C  is  less  than  B ; 

.*.  C  is  less  than  A. 

The  planet  Jupiter  is  greater  than  the  earth ; 
The  earth  is  greater  than  the  moon ; 
.*.  The  planet  Jupiter  is  greater  than  the  moon. 

The  axiom  governing  this  class  of  syllogisms  may  be  stated  thus: 
What  is  greater  than  a  greater  is  greater  still  than  the  thing.10 

What  was  said  in  §  1  respecting  the  elimination  of  Conversion, 
Figure,  and  Mood  is  to  be  applied  also  to  syllogisms  of  comparison. 
We  cannot,  however,  say  as  much  for  the  simplicity  of  this  reasoning. 
For,  be  it  observed,  the  premises  authorize  more  than  the  strictly  logi- 
cal conclusion  states.  This  excess  is  usually  expressed  thus : 
.*.  By  so  much  the  more  is  A  greater  than  C. 

This  sort  of  argument  is  called  a  fortiori,  which  may  be  understood 
to  mean  "  by  a  stronger  reason,"  and  the  conclusion  expressed  thus : 

Therefore  a  fortiori  A  is  greater  than  C. 

Such  a  conclusion  can  be  reached  only  in  the  affirmative  mood ;  so 
we  may  define  the  argument  a  fortiori  to  be  a  mathematical  affirma- 

10  In  pure  mathematics  this  syllogism  is  used  but  rarely  as  compared  with  the 
syllogism  of  equivalence.  We  find,  however,  that  Euclid  demonstrates  by  aid  of 
it  Propositions  vii,  xvi,  xvii,  and  others  of  his  first  book. 


QUANTITATIVE  3.  177 

live  syllogism  in  which  the  premises  contain  less  (or  more)  than  the 
whole  truth.  Logicians  sometimes  distinguish  between  the  reasoning 
a  minore  ad  majus,  and  that  a  majore  ad  minus  ;  but  the  distinction  is 
superficial,  since  one  is  simply  convertible  into  the  other.11 

Let  us  now  examine  analytically  some  miscellaneous  examples.    Our 
typical  syllogism  above  may  be  analyzed  thus : 

A  is  as  much  as  B  (and  more) ; 

B  is  as  much  as  C  (and  more) ; 

.*.  A  is  as  much  as  C  (and  still  more). 

Here  is  a  simple  concrete  example : 

The  tree  is  higher  than  the  man ; 
The  spire  is  higher  than  the  tree ; 
.*.  The  spire  is  still  higher  than  the  man. 

This  may  be  re-dressed  as  follows : 

The  height  of  the  tree  is  greater  than  the  height  of  the  man ; 
The  height  of  the  spire  is  greater  than  the  height  of  the  tree ; 
.'.  The  height  of  the  spire  is  still  greater  than  that  of  the  man. 

These  propositions  may  be  further  analyzed,  thus : 

The  height  of  the  tree  is  as  muck  as  that  of  the  man  (and  more),  etc. 

Very  often  we  do  not  need  the  pleonastic  conclusion ;  in  which  case 
the  argument  may  be  resolved  thus : 

The  sea  is  broader  than  the  lake  ; 
The  ocean  is  as  broad  as  the  sea  (and  more) ; 
.*.  The  ocean  is  broader  than  the  lake. 

Here  the  second  premise  contains  a  surplus  which  is  elided  in  thought. 
The  syllogism  may  then  be  construed  into  Barbara,  by  taking  for 
the  middle  term  "what  is  as  broad  as  the  sea."  It  is  evident  that 
this  treatment  considers  the  judgments  as  compound,  and  views  the 
reasoning  as  complex.  Also,  that  both  kinds  of  judgments  of  degree 
may  occur  in  the  same  reasoning.  Sometimes  the  judgments  are 
triplex,  as : 

A  includes  B ; 

B  includes  C ; 
.'.  A  includes  C. 


11  De  Morgan  gives  a  more  elaborate  analysis  of  this  argument  than  others  of 
our  common  authorities.     See  bis  Formal  Logic,  pp.  20-22. 

12 


178  OF    REASONINGS. 

The  first  premise  says  three  things.  It  says  that  "  A  is  greater  than 
B,"  which  is  compounded  of,  1st,  "  as  much  as,"  and,  2dly,  "  more ;"  also 
it  says,  3dly,  that  u  A  partially  coincides  with,"  or  "  is  the  same  as,  B." 
Not  only  do  both  kinds  of  judgments  of  degree  occur  in  the  same 
reasoning,  but  qualitative  judgments  also  often  combine  with  quantita- 
tive. For  example, — 

The  sun  is  a  star  revolving  about  a  remote  celestial  centre ; 
The  sun  is  the  centre  of  our  system,  controlling  its  secondaries ; 
.'.  Our  system  revolves  about  a  remote  celestial  centre. 

The  form  is — 

M  is  contained  under  P.. . Qualitative. 

M  is  the  same  as  S Quantitative. 

.'.  S  is  contained  under  P Qualitative. 

The  Canon  of  Replacement  is  well  suited  to  such  cases.  Nothing  is 
more  common  in  reasoning  than  to  have  the  minor  premise  declare 
simply  the  equivalence  of  notions,  one  of  which  then  replaces  the 
other  in  the  major  premise  to  constitute  the  conclusion.  The  equiva- 
lence in  such  cases,  however,  amounts  to  identity,  and  should  be  read 
"is  the  same  as." 

We  append  a  single  example  of  reasoning  from  the  mathematical 
whole  to  the  part,  as  follows : 

A  minute  is  a  part  of  a  degree ; 
A  degree  is  a  part  of  a  circle  ; 
.*.  A  minute  is  a  part  of  a  circle. 

§  5.  It  is  sufficiently  manifest  how  readily,  in  a  large  number  of 
cases,  the  quantitative  syllogism  may  be  converted  into  qualitative. 
There  arc,  however,  many  cases  when  this  cannot  be  done  without 
great  violence,  and  some  perhaps  wherein  it  is  wholly  impracticable. 
On  the  other  hand,  qualitative  syllogisms  may  as  often  be  readily 
transmuted  into  quantitative,  sometimes  by  violence,  sometimes  not  at 
all.  The  frequent  practicability  of  this  change  may  have  been  the 
origin  of  so  many  attempts  of  recent  logicians,  they  not  recognizing 
the  fundamental  distinction  of  these  two  wholes,  to  reduce  all  propo- 
sitions to  equations,  proposing  thereby  to  modify,  or  rather  to  super- 
sede, the  whole  Aristotelic  system.  The  best  illustration  of  this  per- 
haps is  Hamilton's  "Unfigured  Syllogism,"12  the  Canon  of  which  has 
already  been  given  in  i,  §  4.  He  says  that  any  syllogism  whatever 

18  See  Appendix  to  his  Logic,  p.  626  ;  cf.  Discussions,  p.  604. 


QUANTITATIVES.  1*79 

may  be  transmuted  as  in  the  following  example,  and  find  adequate 
expression  in  the  unfigured  form  : 

Darii,  Fig.  1,  reduced  to  an  Unfigured  Syllogism. 

All  patriots  are  brave ;          \       f      All  patriots  and  some  brave  men  are  equal ; 
Some  who  flee  are  patriots  >/•  —  •]      Some  who  flee  and  some  patriots  are  equal ; 
.*.  Some  who  flee  are  brave.      )        (  .'.Some  who  flee  and  some  brave  men  are  equal. 

It  will  be  observed  that  the  change  involves  the  quantified  predicate. 
Hamilton  says,  "This  form  has  been  overlooked  by  logicians,  while, 
in  fact,  it  affords  a  key  to  the  whole  mystery  of  syllogism."  Evi- 
dently it  is  only  a  forcing  the  qualitative  reasoning  into  the  quantita- 
tive mould,  and  making  the  expression  needlessly  awkward,  in  order 
to  avoid  even  the  mere  appearance  of  figure.  The  innovation  and  the 
claim  have  been  received  with  a  just  coldness  by  all  except  the  most 
devoted  followers  of  Hamilton. 

§  6.  It  is  needful  to  observe,  before  closing,  that  there  is  another 
class  of  judgments,  one  which  cannot  be  regarded  as  either  qualitative 
or  quantitative.  These  are  causal  judgments.  Besides  the  two  modes 
of  thought  we  have  discussed,  there  is  that  in  which  we  think  events, 
one  as  causing,  bringing  about,  or  determining  another.  With  such 
judgments  we  syllogize,  pursuing  a  train  of  causes  and  effects.  The 
elementary  form  of  this  syllogism  stands  thus : 

A  causes  B ; 

B  causes  C ; 

.*.  A  causes  C. 

This  is  not  reducible  without  violence  to  any  of  the  forms  we  have 
been  considering,  but  logically  it  is  quite  similar  to  the  quantitative 
syllogism.  The  copula  is  " causes"  and,  in  converting,  this  is  to  be 
changed  to  the  notion  of  effect.  Obviously  there  is  no  more  impor- 
tant reasoning  in  life  or  in  science  than  that  which  follows  the  chain 
of  cause  and  effect,  fixing  human  responsibility,  or  explaining  the  facts 
of  nature.  But  the  logic  involved  does  not  seem  to  call  for  special 
discussion  after  what  has  been  said  of  similar  forms.  It  may  be  well 
to  remark,  however,  that  the  copula  is  often  absorbed  in  verb  forms, 
as  "  A  governs  B,"  "  A  lifts  B,"  "  A  excites  B,"  etc.  These,  for 
simplicity's  sake,  may  be  allowed  to  stand  in  the  place  of  the  more 
formal  copula,  provided  the  causal  relation  is  continuously  maintained 
in  the  reasoning.  Just  that  event,  and  no  other,  which  was  the  effect 
of  one  must  be  the  cause  of  the  next,  and  so  on  in  a  chain  throughout 
the  series  of  propositions. 


180  OF    REASONINGS. 

§  7.  Praxis,  Name  the  class  to  which  each  of  the  following  rea> 
soilings  belongs.  Supply  any  lacking  proposition.  Re-dress,  if  need 
be,  analytically,  and  exhibit  the  copula.  Explicate  the  several  syllo- 
gisms that  may  be  involved  in  one  example.  Construe  two  or  three 
as  qualitative : 

1.  The  favorite  pupil  of  the  Academy  was  Aristotle: 
Aristotle  became  the  head  of  the  rival  Lyceum ; 

.-.  Plato's  favorite  became  his  rival. 

2.  The  author  of  Athalie  was  the  greatest  French  dramatist ; 
Racine  was  the  author  of  Athalie ; 

:.  Racine  was  the  greatest  French  dramatist. 

3.  The  sting  of  death  is  sin ; 

And  the  strength  of  sin  is  the  law. — 1  Cor.  xv,  56. 

4.  John  knew  more  than  Peter ; 
Peter  knew  more  than  Mark ; 

.-.  John  knew  more  than  Mark. 

5.  Aristotle  lived  after  Plato ; 
Plato  lived  after  Socrates ; 

.-.  Aristotle  lived  after  Socrates. 

6.  Virginia  is  one  of  the  Southern  States ; 

The  Southern  States  are  a  part  of  the  Union  ; 
.*.  Virginia  is  a  part  of  the  Union. 

7.  All  the  vexations  of  this  life,  including  the  most  petty,  are  not  as 

numerous  as  its  duties ; 
Its  duties  are  its  delights ; 
/.  The  vexations  of  life  are  less  than  its  delights. 

8.  Lias  lies  above  Red  Sandstone ; 
Red  Sandstone  lies  above  Coal ; 

/.  Lias  lies  above  Coal.13 

9.  Wisdom  is  more  precious  than  rubies; 
And  rubies  than  gold ; 

/.  Wisdom  is  of  yet  higher  value  than  gold. 
10.  A  follows  B; 
BfollowsC; 
/.  A  follows  C. 

13  This  example  is  given  by  Whately  without  remark.  It  has  been  a  sore  trou- 
ble to  his  successors.  See  Fowler's  Deductive  Logic,  pp.  168-70,  for  what  the  head 
of  Lincoln  College,  Oxford,  thinks  about  it ;  and  compare  Dr.  McCosh's  summary 
treatment  of  it  in  his  Logic,  p.  144. 


QUANTITATIVES.  181 

11.  If  God  so  clothe  the  grass  of  the  field, shall  he  not  much 

more  clothe  you? — Matt,  vi,  30. 

12.  The  orbit  of  Venus  is  within  that  of  the  earth; 
And  this  within  that  of  Jupiter ; 

.*.  The  orbit  of  Venus  is  within  that  of  Jupiter. 

13.  The  radius  perpendicular  to  a  chord  bisects  the  chord  and  tlie 

subtended  arc.  For  in  the  right-angled  trian- 
gles A  I)  C  and  B  D  C,  A  C  is  equal  to  C  B, 
since  all  radii  are  equal  to  each  other,  and  D  C 
is  common ;  hence  A  D  is  equal  to  B  D ;  for 
if  two  right-angled  triangles  have  the  hypothe- 
nuse  and  a  side  of  the  one  equal  to  those  of 
the  other,  the  third  sides  are  equal.  (Prove 
also  syllogistically  the  rest  of  the  Proposition.) 

14.  The  dome  is  under  the  sky; 
The  altar  is  under  the  dome ; 

.'.  The  altar  is  under  the  sky. 

15.  Behold,  the  heaven  and  heaven  of  heavens  cannot  contain  thee; 

how  much  less  this  house  that  I  have  builded. — 1  Kings  viii, 
27. 

1 6.  To  practise  self-denial  is  to  overcome  temptation ; 
To  overcome  temptation  is  to  conquer  Satan ; 

.*.  Self-denial  is  a  mastery  of  Satan  also. 

17.  If  two  straight  lines  cut  each  other,  the 

vertical  or  opposite  angles  will  be 
equal.  For  the  angles  0  E  A  and 
A  E  D  are  together  equal  to  two  right 

angles,  since  the  angles  which  one  straight  line  makes  with  an- 
other upon  one  side  of  it  are  together  equal  to  tw7o  right  angles ; 
and  the  angles  A  E  D  and  DEB  are  together  equal  to  two 
right  angles  for  the  same  reason;  therefore  the  two  angles 
C  E  A  and  A  E  D  are  together  equal  to  the  two  angles  A  E  D 
and  DEB.  Take  away  the  common  angle  A  E  D,  and  the 
remaining  angle  C  E  A  is  equal  to  the  remaining  angle  DEB. 
In  the  same  manner  it  can  be  demonstrated  that  the  angles 
C  E  B  and  A  E  D  are  equal.  Therefore  if  two  straight  lines, 
etc.  Q.  E.  I).— Euclid,  Prop,  xv,  bk.  i. 

18.  Cocoanuts  contain  milk; 
These  barrels  contain  cocoanuts ; 

/.  These  barrels  contain  milk. 


182  OF    REASONINGS. 

1 9.  Pilate's  dictator  was  the  servile  mob ; 

The  multitudes  cried  with  one  voice,  "  Crucify  him ;" 
/.  They  who  thus  judged  were  the  masters  of  the  judge. 

20.  For  if,  when  we  were  enemies,  we  were  reconciled  to  God  by  the 

death  of  his  Son ;  much  more,  being  reconciled,  we  shall  be 
saved  by  his  life. — Rom.  v,  10. 

21.  It  were  better  to  have  no  opinion  of  God  at  all  than  such  an 

opinion  as  is  unworthy  of  him;  for  the  one  is  unbelief,  the 
other  is  contumely ;  and  certainly  superstition  is  the  reproach 
of  the  Deity. — Bacon,  Essay  xvii. 


COMPOUND    AND    DISGUISED    FORMS.  183 


IV.  COMPOUND  AND  DISGUISED  FORMS. 

§  1.  The  reasonings  thus  far  considered  are  simple.  Under  the 
present  topic  are  to  be  examined  a  few  varieties  of  compound  or 
complex  and  disguised  reasonings.  The  varieties  are  endless,  and 
only  some  of  the  most  important  and  illustrative  can  be  here  de- 
scribed. As  preparatory  to  this,  however,  it  is  needful  to  give  an  ac- 
count of  certain  irregularities  which  obtain  in  the  ordinary  statement 
of  reasoning. 

The  deviation  of  propositions  from  strict  logical  form  gives  rise  to 
a  very  common  kind  of  irregularity.  Simple  propositions  often  take 
irregular  forms ;  e.  g.,  "  It  rains."  Very  common  are  inversions. 
Complex  propositions  are  continually  occurring  in  which  there  is  a 
displacement  of  a  clause.  E.  g.,  "  In  these  sentences  themselves  the 
cases  are  exemplified  which  they  state."  The  use  of  such  proposi- 
tionstconceals  or  complicates  the  logical  forms;  but  this  may  be  more 
than  compensated  by  the  heightened  rhetorical  effect.  A  cause  of 
still  greater  intricacy  is  the  use  of  compound  propositions.  This  we 
shall  consider  more  fully  in  the  sequel. 

The  order  of  the  propositions  being  unessential,  it  is  varied  at  will. 
E.  g.,  "The  fact  that  I  defended  him  is  proof  that  I  held  him  inno- 
cent ;  for  who  would  defend  the  guilty  ?"  Here  the  major  premise 
is  implied  by  the  question,  and  is  stated  after  the  conclusion.  It  is 
quite  usual  to  state  the  conclusion  first,  followed  by  an  illative,  as 
for,  since,  because,  is  proved  by,  etc.  E.  g.,  "  Not  every  passion  is 
blameworthy ;  for  anger  is  a  passion,  and  there  is  a  righteous  anger." 

Except  in  treatises  on  Logic,  it  is  seldom  that  a  formal  syllogism 
occurs.  In  ordinary  conversation,  or  even  in  avowed  argumentation, 
its  presence  is  apt  to  be  an  offence  to  the  hearer  or  reader.  He  natu- 
rally expects  to  have  some  small  share  in  the  thinking;  whereas  the 
syllogism  leaves  him  none,  and  charges  him  with  a  minimum  of  in- 
telligence. The  intelligent  mind  often,  on  the  barest  suggestion, 
catches  a  thought,  and  sweeps  through  a  train  of  reasoning  with  mar- 
vellous rapidity  and  accuracy.  Hence  the  more  cultivated  the  hearer, 
the  less  need  is  there  of  elaborate  statement.  A  hint,  perhaps,  is  all 
that  is  required  for  cogent  conviction ;  whence  the  old  saw  "  A  word 


184  OF    REASONINGS. 

to  the  wise  is  sufficient."  Besides,  a  logically  formal  statement  would 
render  the  expression  of  almost  any  thought  intolerably  prolix.  Brief 
expression  is  not  only  more  pleasing  and  forcible,  but  often  more 
clear.  Unnecessary  words  do  not  elucidate,  but  obscure,  thought. 
It  is  best,  then,  to  use  no  more  than  are  needful  to  convey  the 
thought  clearly  and  distinctly.  For  these  reasons  it  is  customary 
greatly  to  abbreviate  expression.  Essential  propositions,  such  as  are 
obvious,  are  elided ;  others  are  compounded  or  condensed  in  various 
ways,  so  that  they  rarely  state  the  thoughts  entire,  nor,  indeed,  accord- 
ing to  their  actual  order.  The  Enthymeme  is  the  usual  form  of  brief 
statement ;  and  since  reasonings  so  frequently  appear  in  this  guise,  we 
will  devote  the  rest  of  this  prefatory  section  to  its  consideration. 

It  is  customary,  then,  to  abridge  syllogisms ;  and  since,  in  that  case, 
some  part  of  the  reasoning  is  in  the  mind  only,  such  statement  is 
called  an  Enthymeme  (f  v  Ouyuw),  which  is  thus  defined :  An  incom- 
plete syllogism,  one  or  two  judgments  being  unexpressed.1  We  may, 
then,  distinguish  four  orders  of  enthymemes,  viz. : 

1st.  The  major  premise  being  unexpressed.  E.  g.,  Sinus  is  a  fixed 
star ;  therefore  it  is  self-luminous. 

2d.  The  minor  unexpressed.  E.  g.,  Prayers  are  often  sinful ;  for 
whatsoever  is  not  of  faith  is  sin. 

3d.  The  conclusion  unexpressed.  E.  g.,  Enoch  pleased  God ;  but 
without  faith  it  is  impossible  to  please  him  (=2 whoever  pleases  God 
has  faith). 

4th.  Only  one  proposition  expressed.  E.  g.,  if  we  see  on  a  tomb- 
stone "  The  memory  of  the  just  is  blessed,"  the  implied  syllogism  is 
sufficiently  manifest.  This  form  often  occurs  in  the  use  of  texts, 
proverbs,  pithy  sayings,  and  in  witticisms.  If  some  one,  seeing  me 
sorely  vexed,  should  say,  "  The  way  of  transgressors  is  hard,"  I  am 
indignant,  for  the  implied  syllogism  concludes  me  a  transgressor,  yet 
falsely,  since  it  has  an  undistributed  middle,  Falstaff,  when  running 
from  the  battle-field,  says,  "  The  better  part  of  valor  is  discretion," 
which  also  is  a  major  premise.  In  the  same  scene  he  exclaims,  in  re- 
ply to  Prince  Hal,  "  Lord,  Lord,  how  this  world  is  given  to  lying !" 
— another  major  premise  conveying  what  we  call  "an  insinuation," 

1  This,  though  an  ancient  view  and  generally  accepted  in  Logic,  is  not  the  en- 
thymeme  of  Aristotle.  With  him  the  enthymeme  is  a  reasoning  of  a  peculiar  mat- 
ter— from  likelihoods  and  signs,  (rvXXoyKTjuoc  t £  t IKUTUV  rj  o7//«/ wv.  See  Anal.  Prior. 
ii,  27;  Rhet.  i,  2;  also  Hamilton's  Logic,  Lect.  xx;  Discus&ians^  p.  153  sq.  (Am, 
ed.) ;  and  Hansel's  Aldrich,  Appendix,  note  F. 


COMPOUND   AND    DISGUISED    FORMS.  185 

the  implied  conclusion.3  The  answer  to  a  question  is  often  indirect, 
i.  e.,  a  premise  from  which  the  doubtful  proposition  follows, — a  very 
satisfactory  mode  of  answer,  since  it  furnishes  also  the  ground  of  the 
opinion.  E.  g.,  "Is  smuggling  a  crime?"  Ans.,  "Whatever  violates 
the  rights  of  society  is  crime."  Again,  when  the  disciples  of  John 
asked  our  Lord,  "  Art  thou  he  that  should  come  ?"  he  replied  indi- 
rectly by  giving  them  a  minor  premise,  not,  however,  in  words,  but  in 
acts.  In  that  same  hour  he  performed  many  miracles,  and  simply 
called  their  attention  to  them.3  The  message  to  Pilate  from  his 
wife  furnishes  an  instance  of  a  single  word,  "just"  suggesting  a 
major  premise,  while  the  conclusion  is  stated  in  the  form  of  an  exhor- 
tation :  "  Have  thou  nothing  to  do  with  that  just  man."  The  suc- 
ceeding sentence  conveyed  a  hint  of  arguments  for  the  proof  of  each 
of  the  premises  on  which  that  conclusion  rested.4  A  minor  premise 
may  stand  alone.  Paul  closed  his  speech  before  Festus  with,  "  I  ap- 
peal unto  Caesar."  The  major  to  this  minor  is,  "  Every  Roman  citi- 
zen appealing  unto  Caesar  is  entitled  to  certain  immunities." &  One 
of  the  propositions  thus  standing  alone  Aristotle  calls  an  enthyme- 
matic  sentence,6  and  quotes  the  following  as  an  example :  'Adararov 
opyrjv  p)  0uAarre,  Qvrirbs  &v.  This  may  be  rendered,  "  O  mortal, 
cherish  not  immortal  hate."  But  the  participial  phrase,  more  strictly 
rendered,  is  "  Being  mortal,"  and  this  constitutes  a  minor  to  the  re- 
mainder, which  is  the  conclusion.  So  it  seems,  in  the  common  log- 
ical view,  to  be  rather  an  enthymeme  of  the  first  kind. 

The  major  premise  is  omitted  more  frequently  than  any  of  the 
other  propositions,  because  it  contains  commonly  a  general  rule,  read- 
ily understood  and  fully  admitted;  whereas  the  minor  premise  is 
quite  commonly  a  question  of  fact  which  needs  to  be  stated  and  es- 
tablished in  order  to  be  subsumed.  E.  g.,  "  A  certain  celestial  body 
exhibits  a  proper  motion  among  the  stars,  therefore  it  is  a  member  of 
the  solar  system."  The  famous  speech  of  Antony  over  the  body  of 
Csesar  consists  of  a  series  of  enthymemes,  the  conclusions  being  only 
suggested.7  This  is  high  art  before  an  audience  whose  favor  is  doubt- 
ful. When  we  permit  the  hearers  to  draw  the  conclusion,  they  then 
feel  the  argument  to  be  somewhat  their  own,  a  feeling  often  more 
convincing  than  the  logic. 

2  Hen.  IV,  act  v,  sc.  4.  9  Luke  vii,  18-22. 

4  Matt,  xxvii,  19.  6  Acts  xxv,  11. 

6  Rhet.  ii,  xxi,  6.  7  Julius  Ccesar,  act  iii,  sc.  2. 


186  OF    REASONINGS. 

§  2.  An  Epichirema,  or  reason-rendering  syllogism,  is  one  that  has 
attached  to  either  premise,  or  to  both,  a  supporting  reason.  That  is 
to  say,  it  is  a  syllogism  having  for  a  premise  the  conclusion  of  an  en- 
thymeme.  This  enthymeme  may,  of  course,  be  expanded  into  a  syl- 
logism. A  syllogism  whose  premise  is  the  conclusion  of  another  is 
called  an  " episyllogism"  One  whose  conclusion  is  the  premise  of 
another  is  called  a  " protyllogism"  E.  g. : 

Episyllogism.  Prosyllogism. 

Vice  is  odious ;  (      Whatever  enslaves  is  a  vice ; 

Avarice  is  a  vice ;  for  it  enslaves ;  —  -|       Avarice  enslaves ; 
.'.  Avarice  is  odious.  (  .*.  Avarice  is  a  vice. 

The  propriety  of  thus,  in  the  progress  of  an  argument,  offering  some 
reason  or  reasons  in  support  of  its  doubtful  propositions  is  apparent. 
By  so  doing  we  avoid  the  necessity  of  returning  over  the  same  ground ; 
and  by  clearing  doubts  as  we  go  along,  we  are  not  so  likely  to  excite 
in  the  hearer  the  disgust  that  comes  of  suspense. 

The  oration  of  Cicero  pro  Milone,  though  not  formally  an  epi- 
chirema,  may  be  viewed  as  one  on  an  extended  scale,  and  an  analysis 
of  it  stated  thus : 

It  is  lawful  to  slay  one  who  lies  in  wait  for  us ;  for  this  is  accord- 
ing to  natural  law ;  moreover,  the  laws  of  all  other  nations  permit 
it ;  and,  in  addition,  we  have  many  precedents  wherein  our  own 
law  has  justified  it. 

Clodius  did  lie  in  wait  for  Milo ;  for  the  known  hostility  of  Clodius 
renders  it  probable ;  again,  his  equipment  of  deadly  weapons  in- 
dicates such  a  design ;  and,  finally,  the  known  murderous  char- 
acter of  his  attendants  also  evinces  this  purpose. 

Therefore,  It  was  lawful  for  Milo  to  slay  Clodius. 

It  is  more  common  for  the  whole  effort  of  an  advocate  to  be  di- 
rected to  the  establishment  of  the  minor  premise,  and  long  speeches 
have  often  no  other  object.  This  suggests  that  the  arrangement  of 
our  criminal  courts  corresponds  to,  or  rather  presents  the  parts  of,  a 
syllogism.  The  judge  expounds  the  law,  which  is  the  major  prem- 
ise in  the  case,  and,  being  fully  established,  requires  no  proof.  The 
prosecutor  endeavors  to  prove  the  minor  premise,  that  "  The  accused 
is  guilty,"  which  the  jury  decides.  If  "  Not  guilty,"  no  conclusion 
follows.  But  if  "  Guilty,"  the  minor  is  established.  Now  the  judge, 


COMPOUND    AND    DISGUISED    FORMS. 


187 


in  pronouncing  sentence,  formally  draws  the  logical  conclusion,  which 
the  sheriff  practically  executes.  Thus  : 

The  law  says  :  —  Whoever  is  guilty  of  murder  shall  suffer  death.  The  judge  expounds. 
The  prosecutor  proves  :  —  The  prisoner  is  guilty  of  murder.  The  jury  decides,  Yea. 
The  judge  sentences  :  —  Therefore  lie  shall  suffer  death.  The  sheriff  executes. 


§  3.  A  Sorites  (o-wpoc^a  heap)  is  a  chain  of  enthymcmes,  holding 
throughout  the  relation  of  prosyllogism  and  episyllogism.  It  is  called 
by  the  Germans  the  chain  syllogism  (Kettenschluss).  It  can,  of  course, 
be  expressed  in  either  quantity,  the  intensive  quantity  being  the  com- 
mon form.  We  give  an  illustrative  scheme  of  the  two  forms. 


The  progressive  or 
Aristotelic  form, 
in  intension. 


SCHEME  OF  SORITES. 


u  ' 


The  regressive  or 
Goclenian  form, 
in  extension. 


Resolution. 

A  is  B ;          a  is  c  ;         a  is  d ; 
B  is  C ;         C  is  D ;         D  is  not  E ; 
.  a  is  c.       .'.  a  is  d.     .'.  A  is  not  E. 


Resolution. 

D  is  not  E ;    c  is  not  e ;      b  is  not  e ; 
C  is  D ;          B  is  C ;  A  is  B ; 

.'.  c  is  not  e.  .'.  b  is  not  e.  .'.  A  is  not  E. 


Example. 

Some  who  are  prosperous  are  avaricious ; 
The  avaricious  are  intent  on  gain; 
The  intent  on  gain  are  discontented; 
The  discontented  are  not  happy ; 
Some  who  are  prosperous  are  not  happy. 


Example. 

No  discontented  men  are  happy  men ; 
All  men  intent  on  gain  are  discont'd  men ; 
All  avaricious  men  are  men  intent  on  gain ; 
Some  prosperous  men  are  avaricious  men ; 
Some  prosperous  men  are  not  happy  men. 


Notation  in  depth. 


A,  — .  ,0:  —  ,C:  —  ,D:  -H  :E 


Notation  in  breadth. 
E:  -H  :D,  —  :C,  —  :B,  —  ,A 


Other  notations  in  breadth. 


D 

C 

B 

pros 

discontented  men 

men  intent  on  gain 

avaricious  men 

perous  men 

188  OF    REASONINGS. 

The  difference  between  these  two  forms  is  a  question  of  order  of 
premises  merely,  and  therefore  non-essential.  We  may  agree,  as  in 
the  case  of  the  syllogism,  to  use  the  first  form  for  intension  and  the 
second  for  extension ;  but  it  is  an  agreement,  nothing  more.  Logicians 
have  disputed  which  should  be  called  progressive,  and  which  regres- 
sive. It  is  merely  a  strife  about  words.  Till  Kant's  time,  the  Aristo- 
telic  form  was  called  regressive,  and  the  Goclenian  progressive.  Kant 
reversed  this.  Afterwards,  Jacobi  restored  it,  followed  by  Krug  and 
other  German  logicians.  The  influence  of  Hamilton,  who  follows 
Kant,  has  fixed  in  all  recent  English  treatises  the  names  as  we  give 
them.  If  we  regard  the  Aristotelic  form  as  expressive  of  intension, 
it  ascends  from  fact  to  law,  and  might  properly  be  called  the  ascend- 
ing form.  If  we  regard  the  Goclenian  form  as  expressive  of  exten- 
sion, it  descends  from  law  to  fact,  and  might  properly  be  called  the 
descending  form. 

The  following  points  should  be  particularly  observed : 

1st.  The  regular  Sorites  has  as  many  middle  terms,  and  hence  resolves 

into  as  many  syllogisms,  as  it  has  premises,  less  one. 
2d.  The  first  proposition  is  the  only  major  premise  that  is  expressed ; 

all  other  premises  are  minors. 

3d.  Each  unexpressed  major  is  the  conclusion  of  the  preceding  syl- 
logism. 

4th.  Only  one  premise  may  be  negative,  and  this  must  come  last  in 
intension  and  first  in  extension  ;  else  illicit  process. 

5th.  Only  one  premise  may  be  particular,  and  this  must  be  the  first 
in  intension  and  the  last  in  extension ;  else  undistributed  middle. 

We  also  remark  that  in  the  scheme  all  the  syllogisms  are  in  Fig.  1. 
Sorites  cannot  occur  in  the  other  figures  throughout.  One  step,  how- 
ever, may  be  in  Fig.  2  or  Fig.  3,  but  only  one,  and  it  must  be  either 
the  first  or  the  last.  This,  against  Hamilton,  is  established  by  Mill.8 
But,  in  apparent  contravention  of  this  and  others  of  the  above  rules, 
two  sorites  of  different  form  may  be  connected  into  a  continuous  chain. 
The  forms  may  be  found  in  Schuyler's  Logic. 

The  word  "  Sorites "  was  originally,  and  is  still  retained  as,  the 
name  also  of  a  special  fallacy. 

8  See  Hamilton's  Logic,  p.  619;  and  Mill's  Examination  of  Hamilton,  vol.  ii,  p. 
226  sq.  Mill,  rather  harshly,  says :  "  If  Sir  W.  Hamilton  had  found  in  any  other 
writer  such  a  misuse  of  logical  language  as  he  is  here  guilty  of,  he  would  have 
roundly  accused  him  of  total  ignorance  of  logical  writers." 


COMPOUND    AND    DISGUISED    FORMS.  ISO 

§  4.  Our  limited  space  will  admit  of  only  a  few  examples  of  the 
usual  way  in  which  actual  arguments  are  abbreviated,  cumulated,  and 
compounded,  and  of  the  fact  that  all  may  be  resolved  into  simple  syl- 
logisms. Such  illustrations  are  needful,  however,  in  order  to  confirm 
the  preceding  statements,  and  show  with  practical  emphasis  that  the 
simple  syllogism  is  truly  the  unit  of  elaborate  reasonings. 

The  student  of  Logic  should  exercise  himself  in  the  reduction  of  se- 
lect arguments  to  syllogistic  statement.  In  most  cases  he  will  find 
this  no  easy  task,  a  nice  discrimination  being  requisite  to  discern  and 
eliminate  the  merely  rhetorical  elements,  and  to  bring  out  all  the 
proof,  much  of  which  is  often  suggested  rather  than  expressed.  He 
is  advised  to  begin  by  stating  the  ultimate  conclusion,  and  then  to 
seek  for  the  premises  on  which  it  immediately  rests.  If  a  premise 
requires  proof,  regard  it  as  a  conclusion  from  prior  premises,  and 
search  for  them.  Thus  trace  the  reasoning  backwards  until  the  prem- 
ises are  reached  with  which  the  argument  commences,  not  its  state- 
ment, but  its  proof.  For  the  conclusion  is  often  stated  first,  and 
these  primal  premises  last ;  they  may  occur  in  any  order  of  state- 
ment. 

"  It  will  often  happen  that  the  same  assertion  will  have  been  proved 
by  many  arguments,  and  then  the  inquiry  into  the  truth  of  the  prem- 
ises will  branch  out  accordingly.  In  mathematical  or  other  demon- 
strative reasoning  this  will  of  course  never  take  place,  since  absolute 
certainty  admits  of  no  increase ;  and  if,  as  is  often  the  case,  the  same 
truth  admits  of  several  different  demonstrations,  we  select  the  simplest 
and  clearest,  and  discard  the  rest.  But  in  probable  reasoning  (wherein 
the  premises  are  not  absolutely  certain)  there  is  often  a  cumulation  of 
arguments,  each  proving  the  same  conclusion, — i.  e.,  each  proving  it 
to  be  probable, — and  from  these  we  estimate  the  aggregate  proba- 
bility." 

"Whatcly,  who  makes  these  remarks,  suggests  that  the  student  draw 
out  the  course  of  an  argument  in  the  form  of  a  tree,  or  logical  divi- 
sion, thus : 

Conclusion,  Z  is  X,  proved  by 


Y  is  X 

proved  by 
1 

Z  is  Y 

proved  by 

1 

the  argument                    and  also  by              A  is  Y  ( 
1                                        1 

admitted).    Z  is  A 
proved  by 
etc. 

isX        YisB           CisX        Y  is  C 

190  OF    REASONINGS. 

Our  first  example  is  drawn  from  Austin's  Province  of  Jurisprudence. 
He  states  an  argument  of  the  intuitional  school  of  moralists,  which  he 
combats,  thus :  "  No  opinion  or  sentiment  which  is  a  result  of  ob- 
servation and  induction  is  held  or  felt  by  all  mankind.  Observation 
and  induction,  as  applied  to  the  same  subject,  lead  different  men  to 
different  conclusions.  But  the  judgments  which  are  passed  internally 
on  the  rectitude  or  pravity  of  actions,  or  the  moral  sentiments  or  feel- 
ings which  actions  excite,  are  precisely  alike  with  all  men.  Conse- 
quently, our  moral  sentiments  or  feelings  were  not  gotten  by  our  in- 
ductions from  the  tendencies  of  the  actions  which  excite  them ;  nor 
were  these  sentiments  or  feelings  gotten  by  inductions  of  others,  and 
then  impressed  upon  our  minds  by  human  authority  and  example. 
Consequently,  our  moral  sentiments  are  instinctive,  or  are  ultimate  or 
inscrutable  facts." 

This  argument  consists  substantially  of  a  prosyllogism  and  an  epi- 
syllogism,  which,  using  for  brevity  the  catch-words  of  the  terms,  may 
be  stated  thus : 

Pro.    Inductions  are  not  held  by  all  men  alike ; 

Moral ^entiments  are  held  by  all  men  alike; 
.*.  Moral  sentiments  are  not  inductions. 

Epi.     (All  sentiments  not  inductive  are  instinctive ;) 

Moral  sentiments  are  not  inductive ; 
.*.  Moral  sentiments  are  instinctive. 

The  second  example  we  take  from  the  Epistle  to  the  Romans  viii, 
28-30.  "And  we  know  that  all  things  work  together  for  good  to 
them  that  love  God,  to  them  who  are  the  called  according  to  his  pur- 
pose. For  whom  he  did  foreknow,  he  also  did  predestinate  to  be 
conformed  to  the  image  of  his  Son,  that  he  might  be  the  first-born 
among  many  brethren.  Moreover,  whom  he  did  predestinate,  them 
he  also  called ;  and  whom  he  called,  them  he  also  justified ;  and  whom 
he  justified,  them  he  also  glorified." 

This  is  evidently  a  polysyllogism,  or  sorites,  and  stated  so  nearly  in 
strict  logical  form  that  redressing  is  needless.  Another  premise,  quite 
obvious,  is  to  be  supplied  at  the  close,  thus :  "  And  whom  he  glori- 
fied, they  are  they  to  whom  all  things  work  together  for  good."  The 
strictly  formal  conclusion  then  would  be :  "  Therefore,  whom  he  did 
foreknow,  they  are  they  to  whom  all  things  work  together  for  good." 
More  freely  and  fully  stated,  it  might  read  thus :  "  Therefore,  whom 
he  did  foreknow,  predestinate,  and  call  according  to  his  purpose,  they, 


COMPOUND    AND    DISGUISED    FORMS.  191 

loving  God,  are  they  to  whom,"  etc.  The  apostle  first  affirms  the 
conclusion  and  then  details  its  proof. 

The  third  example,  which  is  rather  a  series  of  examples,  we  draw 
from  Bacon,  Essay  xvi,  "  On  Atheism :"  "  A  little  philosophy  in- 
clineth  man's  mind  to  atheism,  but  depth  in  philosophy  bringeth 
men's  minds  about  to  religion ;  for  while  the  mind  of  man  looketh 
upon  second  causes  scattered,  it  may  sometimes  rest  in  them,  and  g;o 
no  further;  but  when  it  beholdeth  the  chain  of  them  confederate  and 
linked  together,  it  must  needs  fly  to  Providence  and  Deity." 

Here  are  two  adversative  enthymemes  stated  together.  They  easily 
explicate  thus : 

The  mind,  looking  upon  second  causes  scattered,  may  rest  in  them  ; 
(The  shallow  philosopher  does  this ;) 
.*.  The  shallow  philosopher  may  be  atheistically  inclined. 

But  The  mind  that  comprehends  the  chain  of  causes  linked  must  fly  to  Deity ; 

(The  profound  philosopher  does  this ;) 
.*.  The  profound  philosopher  must  believe  in  God. 

A  little  further  on,  Bacon  says,  "It  appearcth  in  nothing  more 
that  atheism  is  rather  in  the  lip  than  in  the  heart  of  man  than  by  this, 
that  atheists  will  ever  be  talking  of  that  their  opinion,  as  if  they 
fainted  in  it  themselves,  and  would  be  glad  to  be  strengthened  by  the 
consent  of  others ;  nay,  more,  you  shall  have  atheists  strive  to  get  dis- 
ciples, as  it  fareth  with  other  sects ;  and,  which  is  most  of  all,  you 
shall  have  them  that  will  suffer  for  atheism,  and  not  recant ;  whereas, 
if  they  did  truly  think  that  there  were  no  such  thing  as  God,  why 
should  they  trouble  themselves  ?" 

Here  the  argument  is  cumulative,  the  same  conclusion  being  sup- 
ported by  at  least  two  sets  of  premises,  thus : 

(Those  ever  seeking  to  be  strengthened  by  the  consent  of  others  do  not 

believe  heartily ;) 
Atheists  are  ever  seeking  this ; 
.*.  Atheists  do  not  believe  at  heart  what  is  on  their  lips. 

Moreover,  (Those  who  at  heart  do  not  believe  in  God  can  have  no  occasion  to 
trouble  themselves  to  win  disciples,  or  to  suffer  for  opinion's  sake;) 
Atheists  do  find  occasion  thus  to  trouble  themselves ; 
.*.  Atheists  do  not  believe  heartily  there  is  no  God. 

Again,  further  on,  we  find:  "They  that  deny  a  God  destroy  a 
man's  nobility ;  for  certainly  man  is  of  kin  to  the  beasts  by  his  body ; 


192  OF    REASONINGS. 

and  if  he  be  not  of  kin  to  God  by  Ins  spirit,  he  is  a  base  and  ignoble 
creature." 

(What  is  of  kin  to  beasts  and  not  to  God  is  base  and  ignoble ;) 
Man  is  of  kin  to  beasts  and  not  to  God ; 
.'.  Man  is  base  and  ignoble. 

But  (Who  thus  deny  man's  kinship  with  God  make  man  ignoble ;) 

(They  that  deny  a  God  must  deny  this  kinship  ;) 
.*.  They  destroy  man's  nobility. 

"Atheism  destroys  likewise  magnanimity  and  the  raising  human 
nature ;  for  take  an  example  of  a  dog,  and  mark  what  a  generosity 
and  courage  he  will  put  on  when  he  finds  himself  maintained  by  a 
man,  who  to  him  is  instead  of  a  god,  or  melior  natura, — which  courage 
is  manifestly  such  as  that  creature,  without  that  confidence  of  a  better 
nature  than  his  own,  could  never  attain.  So  man,  when  he  resteth 
and  assureth  himself  upon  divine  protection  and  favor,  gathereth  a 
force  and  faith  which  human  nature  in  itself  could  not  obtain ;  there- 
fore, as  atheism  is  in  all  respects  hateful,  so  in  this,  that  it  depriveth 
human  nature  of  the  means  to  exalt  itself  above  human  frailty." 

The  above  might  perhaps  be  construed  as  in  part  an  argument  from 
analogy;  but  it  would  seem  that  the  example  of  "a  dog"  serves 
rather  to  illustrate  the  wide  universality  of  the  major  premise. 

Any  being,  even  a  dog,  maintained  by  melior  natura,  gathers  a  strength  unat- 
tainable in  its  own; 

(Man,  maintained  by  divine  protection  and  favor,  has  the  confidence  of  a  better 

nature  than  his  own ;) 
/.  Man  resting  on  Deity  gathereth  a  force  and  faith  otherwise  beyond  his  reach. 

Now  by  complex  conceptions : 

(Whatever  deprives  man  of  reliance  on  God  deprives  him  of  this 

means  to  exalt  himself  above  human  frailty ;) 
(Atheism  deprives  man  of  reliance  on  God ;) 

.*.  Atheism  deprives  man  of  the  means  to  exalt  himself,  and  so  de- 
stroys magnanimity  and  the  raising  human  nature. 

Eut,furthei;  (Whatever  deprives  man  of  the  means  to  exalt  himself  is  hateful ;) 

Atheism  does  this ; 
.*.  Atheism  is  hateful. 

One  of  Whately's  annotations  on  this  Essay  is  as  follows :  "  How- 
ever imperfectly  and  indistinctly  we  may  understand  the  attributes  of 
God — of  the  Eternal  Being  who  made  and  who  governs  all  things — 
the  '  mind  of  this  universal  frame,'  the  proof  of  the  existence  of  a 


COMPOUND    AND    DISGUISED    FORMS.  193 

Being  possessed  of  them  is  most  clear  and  full ;  being,  in  fact,  the 
very  same  evidence  on  which  we  believe  in  the  existence  of  one  an- 
other. How  do  we  know  that  men  exist  (that  is,  not  merely  beings 
having  a  certain  visible  bodily  form — for  that  is  not  what  we  chiefly 
imply  by  the  word  'man' — but  rational  agents,  such  as  we  call  men)  ? 
Surely  not  by  the  immediate  evidence  of  our  senses  (since  mind  is 
not  an  object  of  sight),  but  by  observing  the  things  performed,  the 
manifest  result  of  rational  contrivance." 

The  prosyllogism  is  an  equivalent  syllogism. 

Pro. — The  proof  that  man  exists  is  the  argument  founded  on  observed  contrivance ; 

(The  proof  that  God  exists  is  the  same  argument ;) 
.'.  The  proof  that  God  exists  is  the  proof  that  man  exists. 

Epi. — (The  proof  that  man  exists  is  most  clear  and  full ;) 

The  proof  that  God  exists  is  the  proof  that  man  exists ; 
.'.  The  proof  that  God  exists  is  most  clear  and  full. 

For  a  fourth  and  final  example,  we  take,  from  the  Appendix  to 
Whately's  Logic,  an  analysis  of  the  first  part  of  Paley's  Evidences, 
somewhat  modifying  and  condensing  the  statement. 

The  ultimate  conclusion  is  established  thus : 

A  religion  attested  by  credible  miracles  is  from  God ; 
The  Christian  religion  is  so  attested  ; 
.*.  The  Christian  religion  is  from  God. 

Of  these  two  premises,  the  minor  was  admitted,  while  the  major 
was  denied  by  unbelievers  in  ancient  times;  whereas  at  present  the 
case  is  reversed.  Paley's  argument,  therefore,  goes  to  establish  the 
minor,  as  follows : 

All  miracles  attested  by  persons  claiming  to  have  witnessed  them, 
— who  pass  their  lives  in  labors,  dangers,  and  sufferings 
— in  support  of  their  statements, 
— and  who  submit  to  new  rules  of  conduct, 
— in  consequence  of  their  belief, 

are  worthy  of  credit ; 

Christian  miracles  are  attested  by  such  evidence ; 
.*.  Christian  miracles  are  worthy  of  credit :  i.  e., 

The  Christian  religion  is  attested  by  credible  miracles. 

The  major  of  this  syllogism,  "  That  a  story  so  attested  is  credible," 
is  supported  by  two  arguments:  1st,  That  it  is  a  priori  improbable 
that  a  false  story  would  be  thus  attested,  since  no  sufficient  motive 
can  be  supposed.  2d,  That  it  is  a  posteriori  improbable,  since  no 

13 


194  OF   REASONINGS. 

other  miraculous  story  whatever  lias  ever  been  so  attested ;  and  hence, 
by  subalternation,  no  false  story  of  miracles  ever  has  been  so  attested. 
The  proof  of  this  last  proposition  bifurcates;  viz.,  concerning  such 
stories  as  have  been,  or  are  likely  to  be,  cited  as  parallels,  it  is  proved 
either,  "  They  are  not  so  attested,"  or  "  They  are  not  properly  miracu- 
lous," being  explicable,  without  questioning  the  veracity  of  the  narra- 
tor, as  hallucinations,  etc. 

The  points  of  the  minor  premise  of  the  syllogism  are  established 
by  a  series  of  arguments : 

— That  the  early  witnesses  for  Christianity  suffered  is  proved : 

1st.  A  priori:  they  were  likely  to  suffer,  since  their  doctrine 

was  an  offence,  and  regarded  as  foolishness. 
2d.  From  profane  testimony. 
3d.  From  Christian  testimony. 
— That  they  suffered  in  support  of  their  statements  is  proved : 

1st.  By  that  they  had  nothing  else  so  to  support  except  the 

claims  of  the  new  religion. 

2d.  By  the  testimony  of  historians,  both  Christian  and  profane. 
— That  they  submitted  to  new  rules  of  conduct,  and 
— That  this  was  a  consequence  of  their  belief  of  their  story,  are 

similarly  proved. 

— That  the  miracles  thus  attested  are  what  we  call  Christian  mira- 
cles is  proved : 
1st.  A  priori:   it  is  unlikely  that  the  original  story  should 

have  been  lost  and  a  new  one  taken  its  place. 
2d.  By  incidental  allusions   of  ancient  writers,  showing   the 
stories  of  these  witnesses  and  of  our  Scriptures  to  be  the 
same. 
3d.  By  the  inherent  credibility  of  our  historical  Scriptures. 

This  last  is  supported  by  a  new  series.  It  will  be  seen  that  much 
of  the  argument  is  cumulative,  a  number  of  reasons  being  cited  to 
prove  the  same  point.  Also  that  in  the  latter  part  of  the  analysis 
each  subsidiary  argument  can  easily  be  turned  into  a  syllogism  by 
supplying  an  obvious  major. 

§  5.  Arguments  are  frequently  stated  in  what  at  first  glance  appears 
to  be  a  single  simple  syllogism,  but  which  a  slight  inspection  discovers 
to  be  compound,  or  at  least  to  involve  some  essential  deviation  from 
rule.  We  will  state  and  analyze  a  few  representative  examples. 


COMPOUND    AND    DISGUISED    FORMS.  195 

When  a  conclusion  is  a  compound  proposition,  it  is  evident  that 
there  must  be  at  least  one  compound  premise,  and  that  the  statement 
involves  two  or  more  syllogisms.  E.  g. : 

The  triumvirs  were  ambitious ; 
CaDsar,  Pompey,  and  Crassus  were  triumvirs ; 
.'.  Caesar,  Pompey,  and  Crassus  were  ambitious. 

Here  are  obviously  three  syllogisms  involved  in  one  statement.  If 
we  substitute  for  the  major  term  "  friends,"  there  are  still  three.  But 
if  we  substitute  "  founded  the  empire,"  then  there  is  but  one,  since  the 
change  makes  all  the  propositions  simple. 

When  the  conclusion  is  simple,  a  compound  premise  involves  a  sur- 
plus of  matter.  E.  g. : 

Whatever  revolves  about  the  earth  must  present  phases ; 
The  moon  alone  revolves  about  the  earth  ; 
.*.  The  moon  makes  phases. 

This  compound  minor  premise  resolves  into  "The  moon  revolves 
about  the  earth,"  from  which  the  conclusion  follows,  and  "  What  is 
not  the  moon  does  not  revolve  about  the  earth,"  from  which  no  con- 
clusion is  competent,  since  it  would  give  illicit  major.  Hence  in  this 
syllogism  more  is  contained  in  the  premises  than  can  be  collected  in 
the  conclusion. 

But  a  compound  exponible  premise  in  other  cases  may  yield  a  com- 
pound conclusion,  which  then  collects  all  that  was  given.  E.  g. : 

Justification  comes  by  faith  alone ; 
Our  highest  hope  is  justification ; 
.*.  Our  highest  hope  comes  by  faith  alone. 

This  may  evidently  be  resolved  into  two  simple  syllogisms  in  Barbara 
and  Celarent.  But  this  is  not  requisite ;  for  we  may  treat  the  com- 
pound propositions  in  such  case  as  if  simple. 

An  exceptive  subject  has  the  effect  to  distribute,  or  rather  to  total- 
ize, the  predicate  of  the  proposition,  for  one  of  its  elements  is  negative. 
The  following  reasoning,  therefore,  though  it  may  be  construed  as 
AAA,  Fig.  3,  is  sound : 

Only  they  who  fail  are  scorned —  afa 

Only  they  who  fail  suffer =afa 

.'.  Only  sufferers  are  scorned ^afa 

This  conclusion  is  sound  on  condition  that  the  middle  is  distributed 
in  both  premises.  In  the  example,  that  it  is  so  is  sufficiently  plain; 
but  in  common  speech  it  is  usual  to  make  the  distribution  more  fully 


196  OF    REASONINGS. 

appear  by  a  sort  of  reduplication,  thus:  "They,  and  only  they,  who 
fail  are  scorned." 

In  the  following  example  also  all  three  propositions  are  compound 
exponibles,  but  its  solution  is  more  intricate. 

Except  the  evil-minded,  all  are  truly  happy ; 
But  none  are  truly  happy  save  the  content  alone ; 
.'.  There  are  none,  except  the  content,  but  those  who  are  evil-minded. 

Redressing  this,  we  have  as  follows : 

All  but  the  evil-minded  are  truly  happy ; 
None  but  the  content  are  truly  happy ; 
.'.  None  but  the  content  are  any  but  the  evil-minded. 

This  is  in  form  Camestres,  but  the  matter  is  compound  throughout, 
the  conclusion  doubly  so.  The  whole  explicates  into  four  syllogisms, 
yielding  the  following  conclusions : 


1.  The  non-content  are  not  non-evil-minded. 

2.  The  non-content  are.  evil-minded. 

3.  The  content  are  non-evil-minded. 

4.  The  content  are  not  evil-minded. 


When  we  explicate  the  syllogisms  giving  the  two  affirmative  conclu- 
sions, we  find  an  undistributed  middle.  Nevertheless,  the  compound 
conclusion  from  which  they  are  evolved  is  competent,  because  the 
effect  of  an  exceptive  subject  is  to  totalize  the  predicate.  In  this 
case,  therefore,  all  contained  in  the  premises  is  collected  in  the  con- 
clusion. Such  an  intricate  form  and  analysis  are,  however,  quite  need- 
less. Any  one  of  the  simple  elementary  syllogisms  will  be  sufficient ; 
for  we  may  from  its  conclusion  immediately  infer,  by  infinitation,  the 
other  three. 

§  6.  There  is  a  class  of  disguised  syllogisms  which,  from  the  vari- 
ous and  unsatisfactory  treatment  these  have  received,  seems  to  have 
been  the  bane  of  writers  on  logic.  The  premises  arc  irregularly  stated. 
They  consist  of  simple  propositions  indeed,  but  require,  in  order  to 
bring  them  under  the  common  logical  rules,  the  substitution  of  equi- 
pollent propositions,  or  else  of  one  or  more  subsidiary  inferences.  In 
some  cases  the  resolution  is  obvious ;  in  others  difficult.  We  cannot 
do  better  than  to  examine  a  few  characteristic  examples. 


COMPOUND    AND    DISGUISED    FORMS.  197 

The  following  from  Arnauld  is  pronounced  by  Jevons  to  be  im- 
practicable : 9 

The  sun  is  a  thing  insensible ; 
The  Persians  worship  the  sun ; 
.*.  The  Persians  worship  a  thing  insensible. 

Here  are  five  terms ;  yet  the  reasoning  is  obviously  very  good.  The 
Canon  of  Replacement  is  directly  applicable,  the  conclusion  being  ob- 
tained by  replacing,  in  the  minor  premise,  "  the  sun  "  by  its  undis- 
tributed genus,  "  a  thing  insensible,"  as  declared  in  the  major  premise. 
But  even  under  the  common  logical  rules  the  resolution  is  very  simple. 
From  the  major  premise  we  may  immediately  infer,  by  complex  con- 
ceptions, "  They  who  worship  the  sun  worship  a  thing  insensible,"  and 
we  then  have  a  perfectly  regular  Barbara. 
The  following  would  hardly  puzzle  a  tyro : 

Whoever  probes  a  wound  is  on  the  verge  of  crime ; 
A  wound  is  probed  by  the  healer ; 
.*.  The  healer  is  on  the  verge  of  crime. 

For  the  passive  minor,  substitute  the  active  form  immediately  inferred, 
"  The  healer  probes  a  wound,"  and  we  have  again  Barbara. 

An  example  involving  an  immediate  inference  in  opposition  is  as 
follows : 

That  riches  are  often  a  bitter  curse  is  true ; 
And  yet  it  is  also  true  that  most  men  desire  riches ; 
.'.  It  is  false  to  say  that  no  men  desire  what  is  often  a  bitter  curse. 

The  syllogism  which  is  slightly  disguised  in  this  is  the  following  Darii : 

They  who  desire  riches  desire  what  is  often  a  bitter  curse ; 
Most  men  desire  riches ; 
.*.  Most  men  desire  what  is  often  a  bitter  curse. 

This  major  premise  is  immediately  inferred  by  complex  conceptions ; 
the  conclusion,  by  opposition ;  for  if  E  is  false,  then  its  contradictory, 
I,  is  true. 

Finally,  we  recall  the  example  formerly  cited  (i,  §  4)  as  directly 
solved  by  the  Canon  of  Replacement.  Aldrich  (p.  99)  pronounces  it 
a  false  syllogism  on  the  ground  that  it  has  five  terms,  and  therefore 
must  be  invalid.  He  is  wrong ;  the  reasoning  is  evidently  very  good. 

The  divine  law  commands  us  to  honor  kings ; 
Louis  XIV  is  a  king ; 
.'.  The  divine  law  commands  us  to  honor  Louis  XIV. 

8  Lessons  in  Logic,  p.  158. 


198  OF    REASONINGS. 

It  is  sufficiently  evident  that  the  middle  term  here  is  "king."  This, 
then,  is  the  true  subject  of  the  major  premise,  which,  being  redressed 
in  a  form  that  may  be  accepted  as  equipollent,  gives : 

All  kings  are  of  those  whom  the  divine  law  commands  us  to  honor ; 
Louis  XIV  is  a  king; 
.'.  Louis  XIV  is  one  whom  the  divine  law  commands  us  to  honor. 

The  conclusion  of  this  Barbara,  again,  is  merely  a  similarly  equipollent 
form  for  "  The  divine  law  commands  us  to  honor  Louis  XIV." 
The  following  treatment  will  to  some  readers  be  more  satisfactory : 

Louis  XIV  is  a  king ; 
— by  transference  to  the  quantitative  whole  and  inverting,  we  get  : 

This  king  is  Louis  XIV  (i.  e.,  the  one  we  are  thinking  of  is  Louis  XIV). 
— by  complex  conceptions,  we  get  : 

Whatever  commands  us  to  honor  this  king  commands  us  to  honor  Louis  XIV ; 
.But  (Whatever  commands  us  to  honor  all  kings  commands  us  to  honor  this  king;) 
.*.  Whatever  commands  us  to  honor  all  kings  commands  us  to  honor  Louis  XIV. 
Now,  The  divine  law  commands  us  to  honor  all  kings ; 
.*.  The  divine  law  commands  us  to  honor  Louis  XIV. 

§  7.  Logicians  have  distinguished,  described,  and  named  certain 
modes  of  arguing,  some  account  of  which  may  be  fairly  included 
under  the  present  topic. 

The  argumentum  ad  rem  is  the  direct  proof  of  the  main  point  in 
question. 

The  reductlo  ad  absurdum  indirectly  proves  an  assertion  by  proving 
the  absurdity  of  its  contradictory.  It  is  much  used  in  geometry.  It 
is  sometimes  called  argumentum  per  impossibile.  The  refutation  of 
an  assertion  may  also  be  accomplished  by  an  inverse  treatment,10  by 
proving  its  contradictory  true.  In  discussions  we  sometimes  hear  the 
remark,  "Your  argument  proves  too  much."  If  an  absurd  conse- 
quence be  shown,  then  either  its  reasoning  is  illogical  or  a  premise  is 
false.  The  argument  from  effects  is  very  similar.  In  a  question  of 
mere  expediency — -as,  for  example,  the  passage  of  a  law  for  the  suppres- 
sion of  intemperance — we  might  argue  from  effects,  and,  showing  that 
they  are  likely  to  be  evil,  and  that  they  had  actually  resulted  in  evil 
in  analogous  or  entirely  similar  cases,  we  might  thus  prove  the  inex- 
pediency of  such  a  measure.  Questions  of  duty  should  always,  if  pos- 
sible, be  determined  a  priori,  without  regard  to  consequences ;  but  in 

10  See  Part  3d,  ii,  §  8. 


COMPOUND    AND    DISGUISED    FORMS.  199 

some  cases  duty  can  be  determined  only  by  considering  the  conse- 
quences of  the  contemplated  line  of  conduct. 

The  argumentum  ad  populum  is  an  appeal  to  such  principles  as  arc 
cherished  by  the  people.  This  indirectly  supports  the  point,  and  is 
legitimate  if  the  principles  are  sound.  But  when  the  appeal  is  to 
passion  or  prejudice,  it  is  a  sign  that  the  speaker  himself  lacks  con- 
fidence in  his  other  arguments. 

The  argumentum  ad  judidum  is  an  appeal  to  the  common  judg- 
ments of  mankind.  We  hear  it  often  in  conversation,  in  the  phrases 
"  Everybody  says,"  "  No  one  thinks,"  etc.  The  argument  may  pos- 
sess great  force.  It  is  one  of  the  strong  supports  of  the  Scottish  doc- 
trine of  Natural  Kealism,  hence  called  the  philosophy  of  common- 
sense.  Aristotle  says,  "What  seems  true  to  all,  that  we  believe  to 
be,  and  nothing  is  more  worthy  of  credit." 

The  argumentum  ad  verecundiam  is  an  appeal  to  authority,  to  some 
venerable  institution,  as  an  established  religion,  to  antiquity,  etc.  E.  g., 
with  the  scholastics  it  was  a  standing  major  premise,  "  Stultum  est 
dicere  Aristotelcm  errare" 

The  argumentum  ad  hominem  is  arguing  on  the  ground  of  an  op- 
ponent. It  is  also  called  argumentum , ex  concesso.  As  all  disputation 
must  proceed  ex  concessis,  we  may  accept  an  opponent's  principles  on 
which  to  base  a  counter-argument,  though,  perhaps,  we  may  believe 
his  principles  false,  our  argument  being  directed  against  him  personal- 
ly, ad  hominem.  Even  if  we  believe  his  principles  sound,  they  may 
not  be  such  as  we  would  use  in  arguing  with  another,  or  with  man- 
kind generally.  The  conclusion  we  establish  is  frequently  not  the  ab- 
solute and  general  one  in  question,  but  one  merely  relative  and  par- 
ticular. We  may  no  more  than  convict  our  opponent  of  inconsist- 
ency, ignorance,  bad  faith,  or  illogical  reasoning.  We  then  can  claim 
a  victory,  but  not  possession  of  the  territory.  Such  a  course  is  often 
necessary  in  order  to  silence  those  who  will  not  yield  to  fair  general 
argument,  or  to  convince  those  whose  weakness  and  prejudices  will  not 
allow  them  to  assign  it  due  weight.  Our  Lord  often  used  this  method 
against  the  Jews.  See,  for  example,  Matt,  xxii,  41-45. 

The  argumentum  a  fortiori  has  already  been  considered  in  iii,  §  4. 
Its  full  form  is :  If  A  is  greater  than  B,  and  B  greater  than  C, 
still  greater  is  A  than  C.  This  is  essentially  mathematical  or  quan- 
titative. It  may  be  described  in  general  as  the  argument  in, which, 
from  an  admitted  and  less  probable  proposition,  one  depending  on  it, 
and  more  probable,  follows  a  fortiori. 


200  OF  REASONINGS. 

§  8.  Praxis.  State  of  each  of  tlie  following  examples  whether  it  is 
a  simple  enthymeme,  or  an  epichirema,  or  a  sorites.  Write  out  the 
syllogisms  implied  in  full  logical  form.  In  case  of  an  epichirema, 
distinguish  the  pro-  and  epi-syllogism. 

1.  Blessed  are  the  merciful;  for  they  shall  obtain  mercy. 

2.  Cunning  cannot  be  a  virtue ;  for  no  virtue  degrades. 

3.  It  is  I ;  be  not  afraid. 

4.  Cogito,  ergo  sum. — See  Hamilton's  Metaphysics,  p.  258. 

5.  Every  man  should  be  moderate ;  for  excess  will  cause  disease. 

6.  Kings,  having  no  equals,  have  no  friends. 

7.  Suppose  ye  that  these  Galileans  were  sinners  above  all  the  Gali- 

leans, because  they  suffered  such  things  ?     I  tell  you  nay. 

8.  Will,  since  it  often  combats  desire,  as  also  it  often  yields  to  it,  is 

not  desire. 

9.  The  flesh  of  ruminants  is  good  for  food,  and  these  animals,  since 

they  have  horns  and  cloven  hoofs,  belong  to  that  class. 

10.  Man,  inasmuch  as  he  is  naturally  selfish,  and  is,  moreover,  liable 

to  desires  and  passions  which  have  no  limits  or  power  of  re- 
straint in  themselves,  needs  the  restraints  of  law. 

11.  Occasional  turbulence,  being  the  less  of  two  evils,  is  preferable  to 

rigid  despotism. 

12.  What  if  a  rule  never  is,  and  a  principle  always  is,  a  law  admitting 

no  exception? 

13.  A  wise  man  is  never  surprised, because  he  is  never  disappointed; 

and  this  is  because  he  forms  no  expectations  that  are  not  placed 
upon  the  most  certain  basis. 

14.  Suppose  a  man  to  say,  "I  dislike  all  foreigners;"  find  a  premise 

which,  with  this  saying,  would  authorize  the  further  assertion, 
"No  foreigner  ought  to  be  liked." 

15.  Whatever  tends  to  withdraw  the  inind  from  pursuits  of  a  low 

nature  deserves  to  be  promoted.  This  classical  learning  does, 
since  it  cultivates  a  taste  for  intellectual  enjoyments. 

1C.  The  Scripture  narratives  are  trustworthy,  because  the  writers  had 
the  means  of  knowing  the  facts;  also,  they  evidently  were  sin- 
cere and  candid ;  and,  besides,  the  narratives  are  consistent. 

17.  All  true  patriots  are  friends  to  religion,  religion  being  the  basis 
of  national  prosperity;  but,  since  their  lives  are  not  in. accord- 
ance with  its  precepts,  it  follows  that  some  great  statesmen  are 
not  friends  to  religion. 


COMPOUND    AND    DISGUISED    FORMS.  201 

18.  Lithium  is  an  element;  for  it  produces  an  alkali,  therefore  is  a 

metal,  and  hence  an  element. 

19.  I  will  not  do  this  act,  because  it  is  unjust;  I  know  that  it  is  un- 

just, because  my  conscience  tells  me  so ;  and  my  conscience  tells 
me  so  because  the  act  is  wrong. 

20.  When  the  observance  of  the  first  day  of  the  week  as  a  religious 

festival  in  commemoration  of  Christ's  resurrection  was  intro- 
duced, it  must  have  attracted  much  attention  ;  for  it  was  a  strik- 
ing innovation.  In  this  case,  since  attention  would  naturally 
lead  to  inquiry  respecting  the  truth  of  the  resurrection,  the 
story  would  surely  have  been  exposed  as  an  imposture  had  it 
been  one. 

Put  the  following  logical  climax  in  the  Goclenian  form,  and  write 
the  circula^  linear,  and  graphic  notation : 

21.  The  prudent  are  temperate; 

The  temperate  are  constant ; 
The  constant  are  unperturbed ; 

The  unperturbed  are  without  sorrow ; 
Those  without  sorrow  are  happy  ; 

.*.  The  prudent  arc  happy. — Seneca,  Epist.  85. 

Put  the  following  in  its  opposite  form,  and  write  the  notations : 

22.  Nothing  which  is  indissoluble  is  mortal ; 

What  has  no  composition  of  parts  is  indissoluble ; 
A  spirit  has  no  composition  of  parts ; 
A  thinking  substance  is  a  spirit ; 
The  mind  is  a  thinking  substance ; 
.*.  The  mind  is  not  mortal. — Plato. 

State  each  of  the  following  as  a  regular  sorites  in  either  form : 

23.  We  must  increase  the  income-tax ;  for  war  has  become  a  necessity, 

and  we  cannot  go  to  war  without  money,  which  can  be  raised 
only  by  taxation.  But  the  only  tax  which  the  resources  of  the 
country  can  bear  is  the  income-tax,  since  it  will  fall  on  the 
richer  part  of  the  population. 

24.  A  demagogue  must  hold  the  people  in  contempt ;  for,  being  a 

favorite  with  them,  he  must  know  how  to  manage  them ;  there- 
fore he  understands  their  weaknesses,  and  his  contempt  must 
follow. 


202  OF    REASONINGS. 

25.  Riches  are  for  spending,  and  spending  for  honor  and  good  actions ; 

therefore  extraordinary  expense  must  be  limited  by  the  worth 
of  the  occasion. — J3acon,  Essay  xxviii. 

26.  That  defalcation  is  fraud,  and  therefore  a  crime,  no  one  will  deny, 

and  neither  this  nor  any  other  crime  should  go  unpunished. 
But  no  one  who  acts  with  good  intent  should  be  punished. 
Now,  all  generous  conduct  is  of  this  character,  and  it  is  generous 
to  credit  freely.  But  many  failures  in  business  are  the  conse- 
quence of  free  credit ;  so  that  not  every  one  who  fails  is  a  de- 
faulter. 

Analyze  the  following  arguments,  stating  the  results  either  as  sim- 
ple syllogisms  or  as  sorites : 

27.  No  agent  more  effectually  imitates  the  natural  action  of  the  nerves 

in  exciting  the  contractility  of  the  muscles  than  electricity 
transmitted  along  their  trunks ;  and  it  has  hence  been  supposed 
by  some  philosophers  that  electricity  is  the  real  agent  by  which 
the  nerves  act  on  the  muscles.  But  there  are  many  objections 
to  such  a  view ;  and  this  very  important  one  among  the  rest, 
that  electricity  may  be  transmitted  along  a  nervous  trunk  which 
has  been  compressed  by  a  string  tied  tightly  round  it,  while  the 
passage  of  ordinary  nervous  power  is  as  completely  checked  by 
this  process  as  if  the  nerve  had  been  divided. —  Carpenters 
Physiology. 

28.  We  are  not  inclined  to  attach  much  practical  value  to  that  analy- 

sis of  the  inductive  method  which  Bacon  has  given  us  in  the 
second  book  of  the  Novum  Organum.  It  is,  indeed,  an  elabo: 
rate  and  correct  analysis.  But  it  is  an  analysis  of  that  which 
we  are  all  doing  from  morning  till  night,  and  which  we  continue 
to  do  even  in  our  dreams. — Macaulay. 

29.  Our  intellectual  part  being  common,  the  reason,  also,  in  respect  of 

which  we  are  rational  beings,  is  common.  This  being  so,  com- 
mon also  is  the  reason  which  commands  us  what  to  do,  and 
what  not  to  do ;  this  being  so,  there  is  a  common  law  also ; 
hence  we  are  all  fellow -citizens;  and  hence  members  of  the 
same  political  community :  and  therefore  the  world  is  in  a  man- 
ner a  state, — Marcus  Antoninus. 

30.  The  general  object  which  all  laws  have,  or  ought  to  have,  in  com- 

mon is  to  augment  the  total  happiness  of  the  community;  and, 
therefore,  to  exclude,  as  far  as  may  be,  everything  that  tends  to 


COMPOUND    AND    DISGUISED    FORMS.  203 

subtract  from  that  happiness ;  in  other  words,  to  exclude  mis- 
chief. But  all  punishment  is  mischief ;  all  punishment  is  in 
itself  an  evil.  Upon  the  principle  of  utility,  if  punishment 
ought  at  all  to  be  admitted,  it  ought  only  to  be  admitted  in  so 
far  as  it  promises  to  exclude  some  greater  evil. — Jeremy  Bentham. 

31.  Because  the  greatest  part  of  men  are  such  as  prefer  their  own 

private  good  before  all  things,  even  that  good  which  is  sensual 
before  whatsoever  is  most  divine ;  and  for  that  the  labor  of  do- 
ing good,  together  with  the  pleasure  arising  from  the  contrary, 
doth  make  men  for  the  most  part  slower  to  the  one  and  proner 
to  the  other  than  that  duty  prescribed  them  by  law  can  prevail 
sufficiently  with  them ;  therefore  unto  laws  that  men  do  make 
for  the  benefit  of  men  it  hath  seemed  always  needful  to  add  re- 
wards, which  may  more  allure  unto  good  than  any  hardness  de- 
terreth  from  it,  and  punishments,  which  may  more  deter  from 
evil  than  any  sweetness  thereto  allureth. — Hooker,  Ecd.  Pol., 
bk.  I,  x,  6. 

32.  How  did  the  barbarians  reason  in  Acts  xxviii,  3-6  ? 

33.  Prove  syllogistically  that  O  cannot  be  a  premise  in  Fig.  1 ;  that  it 

cannot  be  the  major  in  Fig.  2,  nor  the  minor  in  Fig.  3.  Also 
prove  that  in  Fig.  2  the  conclusion  must  be  negative.  Also 
that  in  Fig.  3  the  conclusion  must  be  particular. 

Write  out  the  syllogisms  involved  in  the  following  irregular  and 
compound  forms,  supplying  any  inference  that  may  be  lacking : 

34.  The  French  once  more  are  endeavoring  to  establish  a  republic. 
A  republic  is  a  representative  government ; 

.*.  The  French  once  more  are  endeavoring  to  establish  a  represent- 
ative government. 

35.  The  value  of  money  is  merely  a  purchasing  power ; 
Interest  on  money  is  only  a  reward  of  abstinence ; 

/.  Interest  on  money  is  not  the  value  of  money. 

36.  Now  no  chastening  for  the  present  seemeth  to  be  joyous,  but 

grievous ;  nevertheless  afterwards  it  yieldeth  the  peaceable  fruit 
of  righteousness  unto  them  which  are  exercised  thereby. — 
ffeb.xu,  11. 

37.  I  give  nothing,  solely  because  I  have  nothing  to  give. 

38.  None  are  happy  but  the  virtuous; 

There  are  many  rich  men  who  are  not  virtuous; 
.*.  There  are  rich  men  who  are  not  happy. 


204  OF    REASONINGS. 

39.  Whoever  says,  I  love  God,  and  hateth  his  brother,  is  a  liar ;  for  he 

that  loveth  not  his  brother  whom  he  hath  seen,  how  shall  he 
love  God  whom  he  hath  not  seen  ? 

40.  They  are  out  of  the  reach  of  their  enemies  who  cannot  be  robbed 

of  what  they  love ; 

He  cannot  be  robbed  of  what  he  loves  who  loves  God  alone ; 
/.  They  who  love  God  alone  are  out  of  the  reach  of  their  enemies. 

41.  Every  good  pastor  is  ready  to  give  his  life  for  his  sheep ; 

Now  pastors  in  the  present  day  who  are  ready  to  give  their 

lives  for  their  sheep  are  rare ; 
/.  There  are  in  the  present  day  scarcely  any  good  pastors. 

42.  The  Gospel  promises  salvation  to  the  faithful ; 
Many  whom  the  world  condemns  are  faithful ; 

,\  The  Gospel  promises  salvation  to  many  whom  the  world  condemns. 

43.  Every  one  desires  happiness ;  but  virtue  (alone)  is  happiness ;  hence 

every  one  desires  virtue. — Arist.  Eth.,  bk.  iii. 

44.  Christianity  obligates  servants  to  obey  their  masters  in  those 

things  only  which  are  not  contrary  to  the  law  of  God ; 

But  unlawful  traffic  is  contrary  to  the  law  of  God ; 

Therefore  it  does  not  obligate  them  to  serve  in  an  unlawful  busi- 
ness, but  forbids  them  so  to  do. 

45.  Only  they  who  are  not  conscious  of  guilt  are  not  subject  to  fear; 

thence  it  is  that  conscious  hypocrites  are  always  shy  and  timid, 
while  the  innocent  are  unsuspecting  and  self-possessed. 

46.  Gladstone,  Disraeli,  and  Lord  Derby  are  eminent  statesmen; 
But  they  are  also  eminent  authors ; 

/.  In  some  cases  literary  success  is  not  inconsistent  with  statesmanship. 

47.  (The  commandment  to  sacrifice  is  greater  than  all  others  save  one ;) 
To  love  is  more  than  sacrifice ; 

/.  To  love  God  is  the  greatest  commandment. — See  Mark  xii,  28-34. 

48.  No  man  is  to  be  punished  for  the  crime  of  another  (Netno  puni- 

tur  pro  alicno  delicto) ; — Legal  maxim. 

Nearly  all  of  our  miseries  are  entailed  on  us  by  the  crimes  of  others ; 
.*.  Few,  if  any,  of  our  miseries  are  punishments. 

49.  A  true  philosopher  places  his  chief  happiness  in  moral  and  intel- 

lectual excellence ; 

But  there  is  no  excellence  without  activity ; 

.-.  A  true  philosopher  places  his  chief  happiness  in  moral  and  intel- 
lectual activity. 

50.  Put  Cicero's  episyllogism  (§  2)  in  form,  and  name  the  mood. 


COMPOUND    AND    DISGUISED    FORMS.  205 

What  names  may  be  given  to  the  following  reasonings  ? 

51.  From  a  given  point  in  a  line  only  one  perpendicular  can  be  drawn. 

For  if  a  second  could  be  drawn,  the  angle  which  it  would  make 
with  the  given  line  would  be  a  right  angle  by  definition,  and 
hence  equal  to  that  formed  on  the  same  side  by  the  first  per- 
pendicular; for  all  right  angles  are  equal.  But  one  of  these 
angles  would  be  a  part  of  the  other,  hence  a  part  would  be 
equal  to  the  whole,  which  is  impossible. 

52.  Those  used  by  Demetrius  in  Acts  xix,  23-27  ;  and  by  the  town- 

clerk  in  vers.  35-41. 

53.  Those  used   by   our  Lord  in  Luke  xiii,  15-16;    and  in  John 

x,  34-36. 

54.  Those  used  by  Paul  in  Rom.  v,  7-10. 

55.  That  used  by  Eliphaz  in  Job  iv,  17-19. 


206  OF    REASONINGS. 


V.  CONDITIONALS. 

§  1.  Thus  far  only  categorical  forms  have  been  considered.  The 
common  logical  doctrine  respecting  conditional  forms  is  now  to  be 
stated.  Subsequently  it  may  be  inquired  whether  this  -doctrine  needs 
modification,  and  to  what  extent. 

A  categorical  judgment  predicates  absolutely.  A  conditional  judg- 
ment affirms  relatively  to  some  prerequisite  which  constitutes  a  condi- 
tion. Its  forms  are  primarily  distinguished  according  as  the  condition 
is  expressed  by  means  of  an  antecedent  clause,  or  implied  in  a  disjunc- 
tion, or  both.  Thus : 

f  Categorical e.  g.,  S  is  P,  and  S  is  not  P. 

Judgments  -j  f  Conjunctive ;  e.  g.,  If  A  is  B,  C  is  D. 

(  Conditional  -J  Disjunctive ;  e.  g.,  C  is  either  D  or  non-D. 

(  Dilemmatic ;  e.  g.,  If  A  is  B,  C  is  either  D  or  non-D. 

By  Boethius  "  conditional "  (con-dare,  to  put  together)  is  used  as 
synonymous  with  "  hypothetical "  (vTro-nOevat,  to  place  under),  and 
this,  having  been  usual  with  most  logicians  after  him,  is  adopted 
here.  Each  of  the  three  forms  of  conditionals,  then,  is  also  called  ge- 
nerically  a  hypothetical.  The  word  "  supposition  "  (sub-ponere)  is  the 
Latin  congener  of  "  hypothesis,"  and  synonymous  with  it.  The  dilem- 
matic  proposition,  because  of  its  compound  character,  is  also  called 
the  conjunctive-disjunctive  proposition.1 

§  2.  A  conjunctive  hypothetical  involves  two  clauses,  one  of  which, 
expressing  the  condition,  is  regarded  as  the  subordinate  member,  and 
is  called  the  antecedent,  the  reason,  the  protasis  (Trpo-reiveii',  to  stretch 
before).  The  other,  expressing  the  conditioned,  is  regarded  as  the 
principal  clause  or  member,  and  is  called  the  consequent,  the  apodosis 
(cnrottiSorai,  to  give  back).  Usually  and  formally  the  antecedent  is 
written  first,  but  inversions  are  quite  common. 


1  Hamilton  uses  "  hypothetical "  specifically,  as  synonymous  with  "  conjunctive." 
Hence  he  terms  the  dilemmatic  a  hypothetico-disjunctive  proposition.  See  Logic, 
p.  167.  Whately,  and,  indeed,  except  Mansel,  all  the  Oxford  logicians,  also  Bain 
and  others,  use  "hypothetical"  as  generic,  and  "conditional7'  as  specific. 


CONDITIONALS.  207 

A  complete  enumeration  of  the  conjunctive  forms  is  as  follows: 

1  (a) — If  A  is  B,  A  is  C  ;  c.  g.,  If  man  is  responsible,  he  is  free, 
(b) — If  A  is  B,  C  is  A ;  e.  g.,  If  bliss  has  no  anxieties,  ignorance  is  not  bliss, 
(c) — If  A  is  B,  B  is  C  ;  e.  g.,  If  rubies  are  clay,  some  clay  is  precious, 
(d) — If  A  is  B,  C  is  B ;  e.  g.,  If  metals  are  fusible,  gold  is  fusible. 

2 If  A  is  B,  C  is  D ;  e.  g.,  If  the  wise  are  virtuous,  Socrates  was  innocent. 

In  each  of  the  first  forms  there  are  but  three  terms,  one  being  com- 
mon to  antecedent  and  consequent.  In  the  second  there  are  four. 
Either  clause,  or  both,  may  be  particular,  or  may  be  negative.  The 
consequent  in  1  (b)  must  be  negative,  and  in  1  (c)  must  be  particular. 
This  distinction  of  forms,  based  on  the  number  and  order  of  terms, 
is,  however,  of  no  moment  until  we  come  to  consider  the  ultimate 
analysis  of  hypotheticals.  Until  then  we  are  concerned  only  with  the 
conditional  relation  of  the  clauses,  without  regard  to  their  terms. 
Neither  does  a  partial  identity  of  the  matter  of  the  clauses,  nor  their 
quantity  and  quality,  affect  the  common  logical  doctrine  now  under 
consideration.  In  this  view7,  the  conjunctive  proposition  has  but  one 
form,  expressed  by  any  one  of  the  above  indifferently. 

Upon  grounds  which  will  hereafter  more  clearly  appear,  a  hypothet- 
ical proposition  may  be  converted  by  taking  the  contradictory  of  the 
consequent  as  an  antecedent,  and  the  contradictory  of  the  antecedent 
as  a  consequent.  As  this  is  similar  to  conversion  by  contraposition, 
it  is  called  by  that  name.  We  may  contrapone  l(c)  thus: 
If  no  clay  is  precious,  some  rubies  are  not  clay. 

Again:  If  most  difficulties  are  conquerable,  none  should  be  unattempted; 
Hence,  If  any  should  be  unattempted,  none  are  conquerable. 

§  3.  Disjunctive  propositions  are  those  expressing  that  relation  of 
two  or  more  judgments  in  which  one  must  be  true;  e.  g.,  "Either  C 
is  D,  or  C  is  non-D ;"  usually  abbreviated  into  "  C  is  either  D  or  non- 
D."  Here  neither  D  nor  non-D  is  predicated  absolutely  of  C ;  but 
one  is  affirmed  of  C  on  condition  that  the  other  is  denied.  In  general, 
then,  the  condition  lies  in  the  opposition  of  the  members.  Hamilton 
defines  disjunctives  as  conditionals  having  the  condition  in  the  predi- 
cate ;  but,  e.  g.,  "  Either  he  or  I  am  wrong." 

A  disjunctive  proposition  involves  the  principle,  and  is  subject  to 
the  laws,  of  Division.  It  implies  that  we  have  divided  an  unnamed 
genus  into  co-ordinate  species,  and  it  affirms  the  alternative  identity  of 
an  object  with  one  of  these.  The  opposed  divisions  are  called  the 
disjunct  members,  and  their  relation  to  each  other  the  disjunction. 


208  OF    REASONINGS. 

Disjunctive  judgments,  to  be  strictly  logical,  must  make  a  complete 
disjunction ;  that  is,  the  disjunct  members  must  exhaust  the  divisum, 
and  must  be  exclusive  of  each  other.  They  are  therefore  contradicto- 
ries. The  characteristic  of  contradictory  opposition  is  that  the  oppo- 
sites  cannot  both  be  true  and  cannot  both  be  false :  i.  e.,  one  must  be 
true  and  one  must  be  false ;  hence,  affirming  either  denies  the  other, 
and  denying  either  affirms  the  other.  The  form  is  that  already 

given ;  i.  e., 

Either  C  is  D,  or  C  is  non-D. 

Either  all  wars  are  evil,  or  some  wars  are  not  evil. 

Either  the  prisoner  is  guilty,  or  he  is  not  guilty. 

When  the  division  is  more  than  dichotomous,  we  have  a  series  of 
disparate  terms,  exhaustive  and  coexclusive ;  e.  g., 

C  is  either  D,  or  E,  or  F,  or 

Bodies  are  either  solid,  or  liquid,  or  aeriform. 

Disparates  must  always  be  reduced,  for  logical  treatment,  to  contra- 
dictories by  grouping  them  into  two  opposed  members ;  e.  g., 

Bodies  are  either  solid  or  (liquid  or  aeriform  =)  fluid. 

Angles  are  either  right  or  (acute  or  obtuse  =  )  oblique. 

Less  than  all  the  members  of  a  disparate  series  will  not  yield  a  dis- 
junctive judgment,  since  they  are  not  exhaustive.  Thus,  to  say  "Birds 
are  shot  either  sitting  or  flying  "  is  insufficient,  for  they  may  be  shot 
running  or  swimming.  Hence  contraries,  which  are  the  extreme 
terms  of  a  disparate  series,  cannot  yield  a  disjunctive  judgment.  Thus 
we  cannot  say  "  Men  are  either  black  or  white,"  for  some  are  red, 
and  therefore  the  statement  is  neither  true  nor  logical. 

We  said  above  that,  in  logical  strictness,  the  disjunct  members  must 
also  be  coexclusive.  This  is  true,  but  often  we  make  an  imperfect 
division  wherein  the  species  are  not  coexclusive,  but  intersect,  and 
constitute  communicant  species.  Such  a  division  will  yield  an  im- 
perfect or  incomplete  disjunctive  judgment,  which,  as  it  is  very  com- 
mon, it  is  needful  to  take  into  consideration.  E.  g., 

Jack  is  either  a  fool  or  a  knave. 

We  affirm  he  must  be  one  or  the  other,  but  it  is  also  true  that  he 
may  be  both.  These  terms,  then,  are  not  contradictories.  The  judg- 
ment may  be  formulated  thus : 

Either  C  is  D,  or  C  is  T. 

Here  D  and  T  stand  for  communicant  species.  The  principle  gov- 
erning this  form  is  that  one  must  be  true,  and  both  may  be  true : 


CONDITIONALS. 

hence,  denying  one  affirms  the  other ;  but  affirming  one,  nothing  fol- 
lows.    As  this  is  the  law  of  subcontrary  opposition,  we  will,  for  con- 
venience, distinguish  these  from  contradictory  and  disparate  disjunc- 
tive judgments  as  subcontrary  disjunctive  judgments. 
Disjunctive  judgments  frequently  appear  in  the  form — 

Either  C  is  D,  or  M  is  N. 

Either  Richard  III  was  a  monster,  or  Shakespeare  was  wrong. 

Either  the  patient  has  a  fever,  or  the  doctor  errs,  or  I  mistook  him,  etc. 

Either  Cassar  was  ambitious,  or  Brutus  was  criminal. 

Here  the  matter  of  the  opposed  clauses  is  entirely  distinct.  Such 
a  judgment  is  not  directly  disjunctive,  for  there  is  no  immediate  op- 
position between  the  opposed  clauses.  The  opposition  is  mediate ; 
thus, — 

Either  Richard  III  was  a  monster,  or  he  was  not  a  monster ; 
Bat  If  he  was  not  a  monster,  Shakespeare  was  wrong ; 
Hence,  Either  Richard  III  was  a  monster,  or  Shakespeare  was  wrong. 

The  alternative,  then,  is  declared,  not  between  members  that  are  directly 
opposed,  but  between  one  of  these  and  the  necessary  consequence  of 
the  other. 

Both  conjunctive  and  disjunctive  judgments  always  affirm,  are  al- 
ways positive,  never  negative.  If  we  say  "  C  is  neither  D  nor  E," 
e.  g.,  "  The  boy  is  neither  smart  nor  good,"  this  is  not  to  declare  an 
alternative,  but  is  merely  a  double  denial. 

§  4.  Conjunctive-disjunctive  propositions  are,  as  the  name  indicates, 
compounds  of  the  two  preceding  forms,  and  hence  involve  no  new 
principle.  They  may  be  defined  as  conjunctives  having  a  disjunction 
in  the  consequent,  or  in  the  antecedent,  or  in  both ;  or,  inverting  the 
formula,  they  are  disjunctives  having  a  conjunction  in  one  or  in  both 
members.  Their  forms,  which  are  certainly  subject  to  great  apparent 
variations,  are  usually  represented  as  numerous  and  intricate.  If  there 
are  but  two  disjunct  members,  the  proposition  is  called  dilemmatic 
(oi-Xe/i/m,  a  double  assumption) ;  if  three,  trilemmatic ;  if  four,  te- 
tralemmatic ;  or  if  more  than  two,  polylemmatic.  Ordinarily,  how- 
ever, the  adjective  "dilemmatic"  is  applied  to  all  indiscriminately.8 


8  To  avoid  a  common  confusion,  we  will  use  only  the  adjective  when  speaking  of 
propositions,  restricting  the  use  of  the  nouns  "  dilemma,"  "  trilemma,"  etc.,  to  cer- 
tain syllogistic  forms  hereafter  to  be  described. 

14 


210  OF    REASONINGS. 

In  §  1  we  gave  the  following  abbreviated  form  as  representative: 

If  A  is  B,  C  is  either  D  or  non-D. 
This  may  now  be  expanded  to — 

If  A  is  B,  either  C  is  D,  or  C  is  non-D. 
Again  expanding  we  have — 

Either  if  A  is  B,  C  is  D  ;  or  if  A  is  B,  C  is  non-D. 

This  now  appears  as  a  double  hypothetical  having  the  same  antece- 
dents and  disjunct  consequents. 

Now  let  us  consider  that  a  difference  in  the  matter,  or  in  the  quality 
of  two  clauses,  e.  g.,  "C  is  D,"  and  "C  is  non-D,"  makes  them  distinct 
clauses,  quite  properly  represented  by  "  C  is  D,"  and  "  E  is  F ;" 
for  a  partial  identity  does  not  modify,  except  in  ultimate  analysis, 
the  logical  treatment  of  such  propositions.  Also,  that  a  separate 
representation  of  contradictory  and  subcontrary  opposition  may  be 
omitted,  with  the  understanding  that  every  formal  statement  repre- 
sents either.  Again,  since  disparate  members  must  always  be  grouped, 
for  logical  treatment,  into  two  contradictory  members,  and  since  the 
trilemmatic  and  polylemmatic  forms  are  of  this  nature  and  subject  to 
this  rule,  they  also  may  be  omitted  in  a  classification  of  forms  that  is 
grounded  on  the  relation  of  clauses  rather  than  of  terms. 

Under  these  provisos  we  may  represent  very  easily  an  exhaustive 
statement  of  the  conjunctive-disjunctive  forms,  thus : 

1,  Simple,  (a)— Either  if  A  is  B,  C  is  D ;  or  if  A  is  B,  E  is  F ; 

— having  antecedents  identical  and  consequents  disjunct. 
"       (b>— Either  if  A  is  B,  C  is  D ;  or  if  E  is  F,  C  is  D ; 

— having  antecedents  "disjunct  and  consequents  identical. 

2,  Complex,  —Either  if  A  is  B,  C  is  D  ;  or  if  E  is  F,  G  is  H. 

— having  antecedents  disjunct  and  consequents  disjunct. 

The  following  are  concrete  examples  of  these  forms : 

1  (a) — If  Socrates  was  innocent,  Anytus  was  either  deceived  or  perjured. 

If  we  go  to  war,  we  must  either  contract  a  debt  or  increase  taxation,  or  in- 
demnify ourselves  at  the  enemy's  expense. 
1  (b) — If  man  is  either  well  or  ill  deserving,  he  is  a  moral  agent. 

If  my  king  is  moved,  or  if  he  is  covered,  or  if  I  capture  the  attacking 
piece,  I  am  checkmated  at  the  next  move. 

2 If  the  prisoner  knew  the  consequences  of  his  act,  he  was  criminal ;  or  if  not, 

he  was  insane. 

Either  if  education  is  popular,  compulsion  is  unnecessary ;  or  if  it  is  un- 
popular, compulsion  will  be  resisted ;  or  if  the  people  are  indifferent, 
compulsion  will  be  fruitless. 


CONDITIONALS.  211 

§  5.  "Upon  the  basis  of  the  conditional  propositions  now  described, 
logicians  have  erected  a  system  of  syllogizing  corresponding  in  ter- 
minology with  the  categorical  system.  There  are  then  four  kinds  of 
conditional  syllogisms. 

The  Conjunctive  hypothetical  syllogism  is  one  which  has  for  its 
major  premise  a  conjunctive  proposition,  the  minor  premise  and  con- 
clusion being  the  affirmation  or  denial  of  its  component  clauses.  It 
claims  for  its  canon  the  Law  of  Sufficient  Reason,  modified  thus : 
Every  assertion  must  have  a  ground  or  reason  for  its  support.3  This 
is  explicated  into  two  axioms,  as  follows : 

1.  Asserting  the  reason  asserts  the  consequent. 

2.  Denying  the  consequent  denies  the  reason. 

The  converse  of  neither  axiom,  it  is  said,  is  true.  Denying  the  rea- 
son does  not  deny  the  consequent,  and  affirming  the  consequent  does 
not  affirm  the  reason  ;  for  it  may  follow  from  some  other  reason.  To 
do  either  is  fallacy.  But  we  shall  find  exceptions  to  this. 

The  double  axiom  gives  rise  to  two  so-called  moods.  The  form  of 
the  conjunctive  syllogisms  in  these  two  moods,  and  their  names,  are 

as  follows : 

f      If  A  is  B ;      then       C  is  D ;  \ 

MODUS  POXENS  •<       But  A  is  B ;  But  C  is  not  D ;  >•  MODUS  TOLLENS 

(constructive)    (  .'.  C  is  D.  ',  .'.  A  is  not  B.          )      (destructive). 

If  the  people  are  industrious,  wealth  increases  ; 

PONENS. —     They  are  industrious ;    ',        Wealth  is  not  increasing ; — TOLLENS. 
.'.  Wealth  is  increasing;    ;    .*.  The  people  are  not  industrious. 

The  major  premise,  or  sumption,  is  always  universal  and  affirmative. 
Either  or  both  of  its  clauses  may  be  particular  or  negative ;  but  the 
total  proposition  always  universally  affirms  that  the  antecedent  neces- 
sitates the  consequent. 

It  will  be  observed  that  the  major  premise  only  is  conditional,  both 
the  minor  premise  and  the  conclusion  in  each  of  the  two  moods 
being  categorical.  If  the  conclusion,  or  both  it  and  the  minor  prem- 
ise, were  also  hypothetical,  the  reasoning  would  not  be  conditional, 
but  categorical.  This  paradox  will  be  illustrated  subsequently. 

In  the  conjunctive  syllogism  there  are  only  three  propositions, 
but  there  may  be  four  terms,  as  in  the  given  example.  All  the 
terms  occur  in  the  major  premise.  Hence,  unlike  the  categorical  syl- 
logism, the  minor  premise  introduces  no  new  term,  and  the  conclusion 
may  have  nothing  in  common  with  it. 

3  See  Part  1st,  ii,  §  7. 


212 


OF    REASONINGS. 


There  are  three  RULES  deduced  from  the  axioms,  as  follows : 

1.  The  subsumption  in  Ponens  agrees  with  its  corresponding  clause 
in  quality,  but  may  differ  in  quantity. 

2.  The  subsumption  in  Tollcns  disagrees  with  its  corresponding 
clause  in  both  quantity  and  quality. 

3.  The  conclusion  in  Ponens  agrees,  and  in  Tollcns  disagrees,  with 
its  corresponding  clause  in  both  quantity  and  quality. 

These  disagreements  in  Tollens  are  because  the  only  true  denial  is  by 
the  logical  contradictory.  Let  us,  however,  remember  that  when  the 
subject  is  individual,  as  in  the  previous  example,  contradiction  is 
merely  a  change  of  quality.  In  illustration  of  the  rules,  we  may  take 


the  following : 


If  any  nation  prospers 

SA11  are  prospering ; 
or  Some  are  prospering ; 
or  This  one  prospers ; 
.'.  All  are  benefited. 


all  are  benefited ; 


Some  are  not  benefited  ;      >•  TOLLENS. 
or  That  one  is  not  benefited ;  ) 
.*.  None  are  prospering. 


Negative  clauses,  one  or  both,  do  not  offend  these  principles.  The 
following  is  in  strict  conformity : 

If  A  is  not  B,  then  C  is  not  D  ; 

PONENS,  asserts, —     A  is  not  B ;  j        C  is  D  ;     — TOLLENS,  denies, 
(constructive.)       .'.  C  is  not  D.    !    .'.  A  is  B.  (destructive.) 

If  we  contrapone  a  major  premise,  we  shall  find  that  this  reduces  the 
moods  the  one  to  the  other.  Hence  they  are  fundamentally  the  same, 
which  might  be  inferred  from  the  common  origin  of  the  two  axioms 
evolving  the  two  moods. 

In  reductio  ad  impossibile  it  is  quite  usual  to  state  the  argument 
hypothetically,  and  then  the  tollent  mood  applies,  perhaps  so  obviously 
as  to  be  left  unexpressed;  e.  g.,  "If  we  say  we  have  not  sinned,  we 
make  God  a  liar." 

A  number  of  objections  in  detail  might  be  urged  against  this 
scheme  of  syllogizing.  We  will  be  content  at  present  with  pointing 
out  a  couple  of  exceptions.  Whenever  one  clause  is  the  infinitated 
form  of  the  other,  as  "  If  A  is  B,  A  is  not  non-B,"  or  if  the  antecedent 
is  the  sole  condition  of  the  consequent,  then  the  converse  of  each  ax- 
iom is  true ;  i.  e.,  denying  the  antecedent  denies  the  consequent,  and 
affirming  the  consequent  affirms  the  antecedent.  As  these  forms 


CONDITIONALS.  213 

not  unfrequently  occur,  the  rules  should  provide  for  them.     For  ex- 
am rlo, — 

If  silver  is  legal  tender,  it  cannot  be  refused  in  payment  of  debts. 

If  not  even  one  was  saved,  then  all  were  lost. 

If  he  was  present,  you  certainly  saw  him. 

If  force  is  expended,  an  equivalent  force  is  generated. 

If  the  scheme  is  perfect,  no  exception  will  hold. 

Hamilton  gives  the  following  as  the  Canon  of  the  hypothetical  (i.  e., 
conjunctive)  syllogism  :  "Two  or  more  propositions  being  thought  as 
indeterminate  in  quality,  but  as  in  quality  mutually  dependent,  the 
determination  of  quality  in  the  one  infers  a  determination  of  the 
corresponding  quality  in  the  other." 4  But  this,  on  the  other  hand, 
is  true,  in  its  full  generality,  only  of  the  above  excepted  contradicto- 
ry forms.  Nevertheless,  Hamilton  goes  on  to  say,  "  This  Canon  em- 
bodies and  simplifies  the  whole  mystery  of  hypothetical  syllogisms, 
which  have  been  strangely  implicated,  mutilated,  and  confused  by 
the  logicians."  He  then  proceeds  to  an  elaborate  critical  discussion. 
Mill  says,  "  There  is  a  great  quantity  of  intricate  and  obscure  specu- 
lation, in  our  author's  Lectures  and  their  appendices,  relating  to  dis- 
junctive and  hypothetical  propositions."  a  But  Mill,  like  a  true  critic, 
proceeds  only  in  the  tollent  mood,  leaving  others  to  reconstruct  as 
they  may. 

§  6.  The  Disjunctive  hypothetical  syllogism  is  one  having  for  its 
major  premise  a  disjunctive  proposition,  and  having  the  disjunction 
resolved  in  the  minor  premise  and  conclusion.6  According  to  Hamil- 
ton, it  is  governed  by  the  axiom  of  Excluded  Middle,7  affirming  that 
of  two  contradictories  one  must  be  true  and  the  other  false.  The 


4  Logic,  p.  602.  5  Examination  of  Hamilton,  vol.  ii,  p.  225. 

8  "  Our  Hypothetical  and  Disjunctive  Syllogisms  may  be  reduced  to  the  class  of 
Conditional  Syllogisms.  The  Hypotheti.cals  should  be  called,  as  they  were  by 
Boethius  and  others,  Conjunctive,  in  contrast  to  the  co-ordinate  species  of  Disjunc- 
tive. Hypothetical,  as  a  name  of  the  species,  ought  to  be  abandoned. 

The  Conjunctive  are  conditional,  inasmuch  as  negation  or  affirmation  is  not  ab- 
solutely asserted,  but  left  alternative,  and  the  quality  of  one  proposition  is  made 
dependent  on  another.  The  Disjunctive  are  conditional,  inasmuch  as  a  notion  is 
not  absolutely  asserted  as  subject  or  predicate  of  another  or  others,  but  alterna- 
tively conjoined  with  some  part,  but  only  with  some  part,  of  a  given  plurality  of 
notions,  the  affirmation  of  it  with  one  part  involving  the  negation  of  others." 
(Hamilton's  Logic,  p.  600.)  7  Rather,  of  Duality.  See  Part  1st,  ii,  §  4. 


214  OF    REASONINGS. 

disjunct  members  being  contradictories,  wo  may,  through  affirming 
one,  deny  the  other,  and  vice  versa.  This  yields  two  moods,  each  of 
which  is  double.  They  have  the  following  names  and  forms : 

MODUS 

PONENDO 

TOLLENS. 


MODUS 
TOLLENDO 

C  is  either  D  c 
C  is  not  D  ; 

rE  (=non-D); 
CisD; 

PONENS. 

/.  C  is  E. 

.*.  C  is  not  E  ; 

or 

or 

u 

C  is  not  E  ; 

CisE; 

u 

.*.  C  is  D  i 

.'.  C  is  not  D. 

All  men  are  either  justified  or  under  condemnation ; 


To.  PONENS. — Some  are  not  justified; 
.'.  Some  are  under  cond. 

or 

This  one  is  not  under  cond. 
.*.  He  is  justified. 


Some  are  justified ; — Po.  TOLLENS. 
.*.  Some  are  not  under  cond. 


or 


That  one  is  under  cond. 
.*.  He  is  not  justified. 


The  sumption  (the  whole  proposition,  not  the  clauses)  is  universal 
and  affirmative;  the  subsurnption  may  vary.  The  conclusion  must 
have  the  same  quantity  as  the  subsumption,  and  the  opposite  quality. 

We  shall  hereafter  find  that  every  contradictory  disjunctive  judg- 
ment may  be  reduced  to  two  conjunctives.  Each  conjunctive  yields 
two  moods,  and  the  four  forms  thus  arising  correspond  with  the  four 
disjunctive  forms. 

Negative  clauses  call  for  no  modification  of  the  rules ;  e.  g. : 

Either  C  is  not  D,  or  E  is  not  F ; 
Po.  TOLLENS.  —  But  C  is  not  D,  /.  E  is  F. 

If  the  major  premise  presents  three  or  more  disjunct  members  (dis- 
parate terms),  they  must  be  reduced  to  two  contradictories  before  an 
inference  can  be  drawn.  E.  g. : 

Sciences  are  either  pure,  inductive,  or  mixed ; 

To.  PONENS. —     Astronomy  is  neither  a  pure  nor  an  inductive  science ; 
.*.  Astronomy  is  a  mixed  science. 

A  formal  illustration  is  as  follows : 

Either  C  is  D,  or  E  is  F,  or  G  is  H. 

Now  let  the  first  clause  be  contradictory  of  the  other  two  taken  to- 
gether.    Then : 

To.  PONENS.— C  is  not  D ;  /.  Either  E  is  F,  or  G  is  H. 

"  Neither  E  is  F,  nor  G  is  H :   .'.  C  is  D. 

Po.  TOLLENS. — C  is  D ;  .'.  Neither  E  is  F,  nor  G  is  H. 

"  Either  E  is  F,  or  G  is  II ;  .'.  €  is  not  D. 


CONDITIONALS.  215 

This  doctrine  of  the  disjunctive  syllogism  is  inadequate,  as  it  con- 
siders only  the  contradictory  forms,  not  embracing  the  subcontrary 
forms.  The  modification  needed  is  that  the  latter  conclude  in  the 
ponent  moods,  but  not  in  the  tollent.  E.  g. : 

All  afflictions  are  either  punitive,  or  tentative,  or  disciplinary ; 
To.  PONENS. —     Job's  afflictions  were  neither  punitive  nor  disciplinary ; 
/.  They  were  tentative. 

"  David's  were  not  tentative ; 

.*.  They  were  either  punitive  or  disciplinary  (perhaps  both). 

Israel's,  we  cannot  say,  were  punitive,  and  therefore  not  tenta- 
tive nor  disciplinary ;  for  they  were  not  only  punitive,  but 
also  both  tentative  and  disciplinary. 

There  is  a  syllogism  founded  upon  contraries,  called  by  Arnauld 
the  "Copulative  Syllogism."  A  thing  may  be  either  or  neither  of 
two  contraries,  but  cannot  be  both.  Hence  we  may  reason  thus : 

Ye  cannot  serve  God  and  Mammon ; 
Ye  serve  Mammon ; 
.*.  Ye  do  not  serve  God. 

We  may  have  all  the  disjunct  members  affirmed  of  something,  or 
something  affirmed  of  them.  This  gives  rise  to  other  forms.  Thom- 
son calls  the  disjunctive  syllogism  above  described  "complex,"  and 
gives  the  following  as  examples  of  "pure "  disjunctive  syllogisms : 

Every  body  is  solid,  liquid,  or  aeriform ; 
Solid,  liquid,  and  aeriform  bodies  are  elastic ; 
.*.  Every  body  is  elastic. 

All  sciences  are  either  pure,  inductive,  or  mixed ; 
Astrology  is  neither ; 
.*.  Astrology  is  not  a  science. 

But  manifestly  this  reasoning  is  not  conditional,  but  categorical. 
There  is  no  resolution  of  the  disjunction.  Its  members  constitute  the 
middle  term,  totally  affirmed  in  the  first,  totally  denied  in  the  second. 
The  forms  are  strictly  Barbara  and  Camestres. 

§  7.  The  Conjunctive-disjunctive,  or  dilemmatic,  proposition  being 
a  compound  form,  the  syllogisms  founded  on  it  are  also  compound, 
and  often  very  intricate.  Before  proceeding  to  syllogize,  we  should 
be  careful  to  see  that  the  antecedent  is  a  true  condition  of  the  conse- 
quent. This  is  not  the  case,  for  example,  in  "  If  an  egg  is  good,  it 
will  either  sink  or  swim."  Again,  we  should  see  that  the  disjunction 
is  exhaustive.  In  this  example,  "  If  the  habit  of  virtue  is  of  any  value, 


216  OF    REASONINGS. 

it  must  ensure  either  pleasure,  wealth,  or  fame,"  the  disjunction  is  not 
exhaustive,  for  virtue  may  be  valued  on  other  grounds.  We  should 
further  ascertain  whether  the  disjunct  members  are  contradictory  or 
only  subcontrary.  We  may  then  proceed  to  syllogize,  viewing  the 
proposition  either  as  a  conjunctive  or  as  a  disjunctive. 

If  we  reason  on  the  conjunction  looking  on  the  disjunct  members 
as  a  single  clause,  the  syllogism  is  governed  by  the  principles  ex- 
plained in  §  5  ;  thus : 

Either  if  A  is  B,  C  is  D ;  or  if  A  is  B,  E  is  F ; 

POXENS.—       But  A  is  B ;  j        Neither  C  is  D,  nor  E  is  F ;— TOLLENS. 

/.  Either  C  is  D,  or  E  is  F.     •    /.  A  is  not  B. 

If  the  apostles  taught  falsely,  they  were  either  deceivers  or  deceived. 
PONENS.  —  They  did  teach  falsely ; 


.*.  They  were    either    de- 
ceivers or  deceived. 


They  were  neither  deceivers  )       _, 

nor  deceived.  f 

.'.  They  did  not  teach  falsely. 


These  are  plainly  hypothetical  syllogisms,  one  in  each  mood.  The 
latter,  the  tollent  form,  is  given  by  Kant  and  Wolf  as  a  dilemma,  and 
by  Wallis  and  Mansel  as  a  disjunctive  syllogism.7  But  certainly  it  is 
neither ;  for  it  simply  denies  the  antecedent  through  denying  the  con- 
sequent; it  neither  introduces  a  disjunction  nor  resolves  one.  This 
tollent  form  is  sometimes  called  cornutus,  or  the  horned  syllogism 
(bi-cornis),  "  because  in  the  sumption  the  disjunctive  members  are 
opposed  like  horns  to  the  assertion  of  the  adversary ;  with  these  we 
throw  it  from  one  side  to  the  other  in  the  subsumption,  in  order  to 
toss  it  altogether  away  in  the  conclusion.  Such  a  syllogism  is  very 
easily  abused  for  the  purpose  of  deceiving,  through  a  treacherous  ap- 
pearance of  solidity,  and  from  terrifying  a  timorous  opponent  by  its 
horned  aspect." — Krug. 

It  should  be  remarked  that  while  the  particles  "  either — or"  are  dis- 
junctive, the  corresponding  negatives  "  neither — nor"  are  not  so,  but 
are  conjunctive  or  total.  They  do  not  exclude  one  on  condition  of 
the  inclusion  of  the  other,  but  they  exclude  both  or  all.  They  directly 
deny  both  clauses,  and  consequently  deny  the  existence  of  the  disjunc- 
tion. This  is  not  resolution,  but  annihilation. 


7  See  Hansel's  Aldrich,  p.  109,  note.  He  says  this  form  of  reasoning  is  some- 
times called  a  Dilemma,  but  it  is  a  perversion  of  the  Dilemma  proper,  and  intro- 
duces no  distinction  whatever ;  being  merely  a  common  disjunctive  syllogism,  as  is 
shown  by  Wallis  himcelf  (iii,  ch.  19).  It  is,  in  fact,  the  enumeratio,not  the  com- 
plexio,  of  Cicero. 


CONDITIONALS.  21 7 

Now,  on  the  other  hand,  if  we  reason  on  the  disjunction  involved 
in  the  conjunctive-disjunctive  proposition  looking  on  the  conjunctive 
statement  as  a  single  clause,  the  syllogism  is  disjunctive,  and  governed 
by  the  principles  explained  in  §  6.  Thus,  adopting  for  convenience 
the  abbreviated  form,  we  have : 

If  A  is  B,  either  C  is  D,  or  E  is  F ; 
To.  PONENS.—     But  0  is  not  D ; 
/.  If  A  is  B,  E  is  F. 

If  Socrates  was  innocent,  Anytus  was  either  deceived  or  perjured ; 
But  Anytus  was  not  deceived ; 
.*.  If  Socrates  was  innocent,  Anytus  was  perjured. 

By  denying  that  Anytus  was  perjured,  we  have  another  To.  Ponens. 
If  the  disjunct  members  are,  as  in  this  example,  contradictories,  they 
yield  also  two  forms  in  Po.  Tollens,  or  the  destructive  mood. 

The  conjunctive-disjunctive  syllogism,  now  explained,  although  it 
has  a  dilemmatic  sumption,  is  not  properly  a  dilemma  at  all.  The 
logics  are  full  of  confusion  here,  and  often  mistake  it  for  the  dilemma. 
Thomson,  following  Hamilton,  distinctly  so  names  it,  and  rejects  the 
dilemma  proper  from  Logic.8 

§  8.  The  Dilemma  (or  trilemma,  etc.)  is  a  conditional  syllogism 
having  a  double  (or  triple,  etc.)  conjunctive  premise,  and  a  disjunctive 
premise.  Neither  one  of  its  propositions  is  dilemmatic,  or  conjunctivo- 
disjunctive.  In  the  conjunctive-disjunctive  syllogism  treated  conjunc- 
tively, as  explained  in  the  first  part  of  the  preceding  section,  the  dis- 
junct members  of  the  sumption  are  either  affirmed  both  together  or 
denied  both  together.  But  they  may  be  affirmed  or  denied  disjunc- 
tively. In  this  case  the  existing  disjunction  is  declared  in  the  sub- 
sumption,  and  (in  the  complex  forms)  in  the  conclusion.  It  is  there- 
fore needless  to  state  it  in  the  sumption,  which  then  appears  merely 
as  a  double  conjunctive.  Thus  the  dilemmatic  proposition  is  distrib- 
uted; one  of  its  essential  features,  the  conjunction,  appearing  in  the 
sumption ;  the  other,  the  disjunction,  appearing  in  the  subsumption 
and  conclusion.  It  is,  indeed,  indifferent,  as  the  definition  above  im- 
plies, as  to  which  of  these  shall  be  called  the  sumption  and  which 
the  subsumption ;  but  it  is  usual  to  place  the  double  conjunctive 
first,  and  call  it  the  sumption  or  major  premise. 

'  So  also  Bain.     See  Logic,  p.  121  sq. 


218  OF    REASONINGS. 

The  Dilemma  presents  three  distinct  and  inconvertible  forms,  as 
follows : 

1.  Simple  constructive :         If  A  is  B,  C  is  D  ;  and  if  E  is  F,  C  is  D ; 
PONENS. —  But  either  A  is  B,  or  E  is  F ; 

.'.  C  is  D. 

2.  Complex  constructive :      If  A  is  B,  C  is  D ;  and  if  E  is  F,  G  is  H ; 
PONENS. —  But  either  A  is  B,  or  E  is  F ; 

.'.  Either  C  is  D,  or  G  is  H. 

3.  Complex  destructive :       If  A  is  B,  C  is  D ;  and  if  E  is  F,  G  is  H ; 
TOLLENS. —  But  either  C  is  not  D,  or  G  is  not  H ; 

.'.  Either  A  is  not  B,  or  E  is  not  F. 

It  will  be  observed  that  the  subsumption  in  each  form  declares  a  dis- 
junction between  certain  of  the  components  of  the  conjunctive  sump- 
tion ;  that  in  the  simple  form  the  conclusion  is  categorical ;  and  that 
in  the  complex  it  declares  a  disjunction  between  the  other  components 
of  the  sumption. 

A  single  concrete  example  from  Demosthenes  de  Corona  must  suf- 
fice. It  is  in  the  complex  constructive  form,  as  follows : 

If  JEschines  joined  in  the  public  rejoicings,  he  is  inconsistent ;  if  he  did  not,  he 

is  unpatriotic ; 

But  either  he  did,  or  he  did  not ; 
.*.  Either  he  is  inconsistent,  or  he  is  unpatriotic. 

The  form  of  the  sumption  in  this  example  may  be  expressed  thus : 
If  A  is  B,  A  is  C;  and  if  A  is  not  B,  A  is  D. 

Here  the  first  term  of  each  of  the  clauses  is  the  same,  and  the  antece- 
dents differ  only  by  the  negative.  Nevertheless,  the  form  is  complex, 
corresponding  to  No.  2 ;  for  the  clauses  all  differ  from  each  other 
either  in  matter  or  in  quality. 

There  cannot  be  both  a  simple  constructive  and  a  simple  destructive 
dilemma.  Denying  the  consequents  in  No.  1  gives — 

If  AisB,Cis  D;  andif  E  is  F,C  is  D; 
But  C  is  not  D ; 
.'.  A  is  not  B ;  and  E  is  not  F. 

This,  however,  is  merely  a  double  conjunctive  syllogism  in  Tollens. 

The  following,  much  more  than  the  last,  has  an  appearance  of  being 
the  simple  destructive  form,  corresponding  to  No.  1.  It  is  given  as 
such  by  Fowler,  and  copied  from  him  with  approbation  by  McCosh : 

If  A  is  B,  C  is  D ;  and  if  A  is  B,  E  is  F; 
But  either  C  is  not  D,  or  E  is  not  F; 
.*.  A  is  not  B. 


CONDITIONALS.  219 

But  if  this  be  examined,  it  will  be  found  to  be  No.  1  contraponed, 
and  then  treated  in  Tollens.  Now,  to  treat  a  proposition  in  Ponens, 
and  then  to  treat  its  contraponed  form  in  Tollens,  is  to  do  the  same 
thing.  The  reasoning  in  both  cases  is  the  same.  Hence  this  form 
cannot  be  accepted  as  additional  to  those  given,  it  being  the  same  as 
No.  1,  and  only  slightly  disguised  by  a  rearrangement,  after  contrapo- 
sition, of  the  letters  in  alphabetical  order.  Truly,  it  is  a  simple  de- 
structive dilemma,  which  is  to  say  that  a  simple  dilemma  may  appear 
either  in  the  destructive  or  in  the  constructive  form ';  but,  since  these 
are  essentially  the  same,  we  should  not  reckon  both ;  and  this  is  the 
statement  which  we  are  now  supporting. 

Whately,9  endorsed  by  Mansel,10  says,  "  There  cannot  be  a  simple 
destructive  dilemma,"  that  "  the  destructive  is  always  complex."  This 
is  true  under  his  definition  of  the  dilemma,  as  "  A  syllogism  having 
a  conditional  (i.  e.,  conjunctive)  major  premise  with  more  than  one 
antecedent,  and  a  disjunctive  minor."  But  this  limitation  of  the 
major  premise  is  purely  arbitrary,  and  the  definition  is  too  narrow. 
The  truth  is  that  under  the  proper  definition  there  may  be  either,  but 
not  both. 

In  disputation  an  adversary  is  sometimes  "  caught  on  the  horns  of 
a  dilemma."  If  he  meet  it  by  another  with  an  opposite  conclusion, 
he  is  said  to  "rebut  the  dilemma."  Aristotle  thus  illustrates  it: 
"An  Athenian  mother  said  to  her  son,  Do  not  engage  in  public  af- 
fairs ;  for  if  you  do  what  is  just,  men  will  hate  you ;  and  if  you  do 
what  is  unjust,  the  gods  will  hate  you.  This  the  son  rebutted  by  the 
following  retort :  I  ought  to  enter  into  public  affairs ;  for  if  I  do  what 
is  unjust,  men  will  love  me ;  and  if  I  do  what  is  just,  the  gods  will 
love  me."  Both  these  are  in  the  complex  constructive  form,  and  each 
is  followed  by  an  implied  categorical  syllogism.  The  first  dilemma 
originated  with  Antisthenes  the  Cynic,  who  proposed  by  it  to  excuse 
himself  from  meddling  with  politics. 

9  Logic,  bk.  ii,  ch.  iv,  §  5.  10  Note  in  Aldrich,  p.  108. 


220  OF    REASONINGS. 

§  9.  Praxis.  Specify  to  what  class  each  of  the  following  judg- 
ments belongs,  put  it  in  logical  form,  and  distinguish  its  members. 
If  conjunctive,  into  which  of  the  five  forms  does  it  fall  ?  Contrapone 
four  examples.  If  disjunctive,  is  it  contradictory  or  subcontrary, 
mediate  or  immediate?  If  a  polytomy,  reduce  to  a  dichotomy.  If 
dilemmatic,  is  it  simple  or  complex  ?  Formulate  with  letters.  If  the 
proposition  is  defective,  say  wherein. 

1.  Wherever  there  is  smoke,  there  is  fire.     ( Wherever = If  in  any 

place.) 

2.  If  a  government  is  well  constituted  and  skilfully  administered, 

it  is  promotive  of  the  industry  and  wealth  of  its  subjects. 

3.  If  I  err,  it  is  because  I  am  human ;  for  to  err  is  human.     (Is  this 

good  reasoning?) 

4.  I  will  not  let  thee  go,  unless  thou  bless  me.     (Unless  =  if  not.) 

5.  Until  the  night  come,  we  must  work. 

6.  Is  any  among  you  afflicted,  let  him  pray. 

7.  Lear  is  at  the  hut  or  the  palace.     (Real  difference.) 

8.  Hiawatha  left  his  hut  or  wigwam.     (Nominal.) 

9.  If  the  rebellion  be  not  crushed,  the  king  will  be  dethroned. 

10.  If  virtue  is  voluntary,  then  vice  is. — Aristotle,  N.  Ethics,  bk.  iii. 

11.  Punishment  is  intended  either  to  repress  crime  or  to  reform  the 

criminal.     (Perhaps  both.) 

12.  Neither  flattery  nor  threats  could  prevail. 

13.  If  ye  were  Abraham's  seed,  you  would  do  the  works  of  Abraham. 

14.  Whenever  the  sun  and  moon  attract  in  the  same  line,  the  tides 

are  at  n  maximum.     ( Whenever = If  at  any  time.) 

15.  Either  if  this  is  a  judgment,  it  affirms  or  denies;  or  if  it  is  a  ques- 

tion, it  does  neither. 

16.  Ye  shall  not  eat  of  it,  neither  shall  ye  touch  it,  lest  ye  die. 

17.  If  ye  eat,  ye  shall  die.    Though  ye  eat,  ye  shall  not  die,    (Though 

=even  if.  The  concessive  clause,  introduced  by  "  though,"  etc., 
grants  the  protasis  of  a  sentence  whose  apodosis  is  denied  by  the 
principal  clause.  The  above  means  "  It  is  not  true,  or  it  docs 
not  follow,  that  if  ye  eat,  ye  shall  die.") 

18.  Though  deep,  yet  clear;  though  gentle,  yet  not  dull. 

19.  It  has  not  been  decided  whether  the  war  will  continue  or  not. 

20.  If  Caesar  lives,  he  will  either  rule  or  ruin. 

21.  Those  who  slew  Caesar  are  either  patriots  or  parricides. 

22.  The  sun  moves  round  the  earth,  or  the  earth  moves  round  the  sun. 


CONDITIONALS.  221 

23.  Although  Homer  sometimes  nods,  nevertheless  is  he  the  greatest 

of  poets. 

24.  Aut  amat  aut  odit  mulier  ;  nihil  tertium. — P.  Syrus. 

("A  woman  loves  or  hates;  she  never  thirds  it.") 

25.  If  you  have  failed  to  nourish  the  poor,  you  have  destroyed  them. 

(Si  non  pavisti,  occidisti. — From  Arnauld.) 

26.  If  the  heart  is  right,  the  actions  will  be. 

27.  The  solitary  is  either  a  beast  or  a  god. — Aristotle,  Polit.  i,  cap.  1. 

28.  The  world  will  not  be  happy  until  either  kings  become  philoso- 

phers, or  philosophers  become  kings. — Plato's  Repub. 

29.  If  the  foot-marks  were  made  by  the  prisoner,  he  must  have  worn 

shoes  too  small  for  his  feet. — Ad  ybs. 

30.  Virtue  is  teachable  if  it  is  knowledge. 

31.  If  man  is  either  well  or  ill  deserving,  he  is  a  moral  agent. 

32.  If  the  square  described  upon  one  of  the  sides  of  a  triangle  be 

equal  to  both  the  squares  described  on  the  other  two  sides  of 
it,  the  angle  contained  by  these  two  sides  is  a  right  angle. — 
Euclid,  Prop,  xlviii,  bk.  i. 

33.  There  could  be  no  choice,  were  there  no  difference. 

34.  Nor  pain,  nor  grief,  nor  anxious  fear, 
Invades  thy  bounds. 

35.  This  elegant  rose,  had  I  shaken  it  less, 
Might  have  bloomed  with  its  owner  awhile. 

If  an  example  among  the  following  is  merely  a  proposition,  syllo- 
gize from  it.  If  an  incomplete  syllogism,  complete  it  and  name  the 
kind  and  mood.  If  a  conjunctive-disjunctive,  or  a  dilemma,  classify 
it,  and  formulate  with  letters.  If  defective,  say  wherein. 

36.  If  any  objection  that  can  be  urged  would  justify  a  change  in  the 

established  laws,  no  laws  could  reasonably  be  maintained. 

37.  Mahomet  was  either  an  enthusiast  or  an  impostor; 
He  was  an  enthusiast ; 

.*.  He  was  not  an  impostor. — Gibbon. 

38.  Corn  will  be  dear  if  the  crops  are  bad,  and  they  seem  likely  to 

be  so. 

39.  A  government  cannot  be  at  the  same  time  despotic  and  the  li- 

censer of  a  free  press ; 

But  the  English  government  permits  a  free  press ; 
/.  The  English  government  is  not  despotic. 


OF    REASONINGS. 


40.  If  man  cannot  make  progress  towards  perfection,  we  must  believe 

him  to  be  either  an  incapable  brute,  or  already  divine. 

41.  I  could,  with  justice,  be  accused  of  acting  contrary  to  my  law, 

only  if  I  maintained  that  Mursena  purchased  the  votes  and  was 
justified  in  doing  so.  But  I  maintain  that  he  did  not  buy 
the  votes;  therefore  I  do  nothing  contrary  to  the  law.—  Cicero 
pro  L.  Murcena,  cap.  iii.  (Ramus  cites  this  as  bad  reasoning. 
Was  he  right  ?) 

42.  Unless  matter  can  move  of  itself,  its  first  motion  must  have  been 

given  it  by  a  spiritual  being.  But  matter  cannot  move  itself ; 
therefore,  etc. 

43.  If  pain  is  severe,  it  will  be  brief ;  and  if  it  last  long,  it  will  be 

slight ;  hence  it  should  be  borne  patiently. 

44.  If  the  system  of  the  universe  is  not  the  best  possible,  we  must 

suppose  that  the  Creator  did  not  prefer  a  better,  or  that  he 
knew  none  better,  or  that  he  could  not  create  a  better.  But  we 
can  entertain  neither  of  these  suppositions,  for  we  should  there- 
by limit  his  goodness,  his  intelligence,  or  his  power.  Therefore 
the  system  of  the  universe  is  the  best.  (Thomson,  Outline, 
§  109,  quotes  this  as  a  trilemraa.  McCosh,  Logic,  p.  150,  like- 
wise. Are  they  right  ?) 

45.  Whether  Logic  be  regarded  as  a  means  of  mental  discipline  or  as 

a  practical  guide  in  reasoning,  it  ought  to  be  studied.  But  it  is 
both.  Hence — what  ? 

46.  If  this  man  were  wise,  he  would  not  speak  irreverently  of  Script- 

ure in  jest ;  and  if  he  were  good,  he  would  not  do  so  in  earnest; 
But  he  does  it  either  in  jest  or  in  earnest ; 
/.  Either  he  is  not  wise,  or  he  is  not  good. 

47.  If  the  books  in  the  Alexandrine  Library  be  in  conformity  with 

the  doctrines  of  the  Koran,  there  is  no  need  of  them  ;  if  adverse, 
then  also  they  should  be  burned. 

48.  If  classical  education  is  worth  the  cost,  either  it  must  be  pre-emi- 

nently fitted  to  develop  the  mental  powers,  or  it  must  furnish 
exceedingly  valuable  information.  But  neither  alternative  can 
be  maintained,  and  so  classical  education  is  not  worth  the  cost. 
(This  is  given  by  Bain,  Logic,  p.  122,  as  a  dilemma.  Right?) 

49.  If  any  satisfactory  theory  could  be  framed  to  explain  the  estab- 

lishment of  Christianity  by  human  causes,  such  a  theory  would 
have  been  proposed  before  now ;  but  no  such  theory  has  ever 
been  proposed  ;  hence,  none  can  be  framed. 


CONDITIONALS.  223 

50.  The  greater  angle  of  every  triangle  is  subtended  by  the  greater 

side,  or  has  the  greater  side  opposite  to  it. 

Let  A  B  C  be  a  triangle,  of  which  the  an- 
gle B  is  greater  than  the  angle  C ;  then 
the  side  A  C  is  likewise  greater  than  the 
side  A  B. 

For  if  AC  be  not  greater  than  AB,  it  must  be  either  equal  to  or 
less  than  A  B.  But  A  C  is  not  equal  to  A  B,  because  then  the 
angle  B  would  be  equal  to  the  angle  C,  the  angles  at  the  base 
of  an  isosceles  triangle  being  equal,  by  Prop,  v :  but  it  is  not ; 
therefore  AC  is  not  equal  to  AB.  Neither  is  AC  less  than 
A  B ;  because  then  the  angle  B  would  be  less  than  the  angle  C, 
the  greater  side  of  every  triangle  having  the  greater  angle  op- 
posite to  it,  by  Prop,  xviii :  but  it  is  not ;  therefore  A  C  is  not 
less  than  AB.  And  it  has  been  shown  that  AC  is  not  equal 
to  AB;  therefore  A  C  is  greater  than  AB.  Wherefore  the 
greater  angle,  etc.  Q.  E.  D. — Euclid,  Prop,  xix,  bk.  i. 

51.  The  ancients  were  in  genius  either  superior  to  the  moderns,  or 

inferior,  or  equal. — See  Hamilton's  Logic,  p.  234. 

52.  If  the  world  existed  from  eternity,  there  would  be  records  prior  to 

the  Mosaic ;  and  if  it  were  produced  by  chance,  it  would  not 
bear  marks  of  design.     But  there  are  no  records  prior  to  the 
Mosaic,  and  the  world  does  bear  marks  of  design. 
.*.  The  world  neither  existed  from  eternity,  nor  is  it  the  work  of 
chance. 

53.  If  the  prisoner  is  to  be  legally  discharged,  either  the  magistrate 

must  refuse  to  commit,  or  the  grand  jury  reject  the  bill,  or  the 
petit  jury  acquit,  or  the  governor  exercise  the  prerogative  of 
pardon.  But  neither  can  the  magistrate  refuse  to  commit,  nor 
the  grand  jury  reject  the  bill ;  hence — what? 

54.  If  a  man  cannot  be  virtuous,  he  must  be  either  unable  to  know 

what  is  right,  or  unable  to  will  what  is  right.  But  he  is  not 
unable  to  know  what  is  right,  for  he  is  intelligent ;  nor  unable 
to  will  what  is  right,  for  he  is  free. 

55.  If  there  be  no  future  life,  then  either  virtue  receives  its  due  re- 

ward in  the  present  world,  or  there  is  no  perfect  government 
administered  among  men,  neither  of  which  is  admissible. 

56.  The  hope  of  immortality  is  either  a  rational  expectation  or  an  il- 

lusion ;  but  that  belief  cannot  be  an  illusion  which  all  the  most 
enlightened  peoples  have  adopted. 


224  OF    REASONINGS. 

57.  If  Christ  be  preached  that  he  rose  from  the  dead,  how  say  some 

among  you  that  there  is  no  resurrection  of  the  dead  ?  But  if 
there  be  no  resurrection  of  the  dead,  then  is  Christ  not  risen ; 
and  if  Christ  be  not  risen,  then  is  our  preaching  vain,  and  your 
faith  is  also  vain.  Yea,  and  we  are  found  false  witnesses  of 
,  God,  because  we  have  testified  of  God  that  he  raised  up  Christ : 

whom  he  raised  not  up,  if  so  be  that  the  dead  rise  not.  For  if 
the  dead  rise  not,  then  is  not  Christ  raised :  and  if  Christ  be 
not  raised,  your  faith  is  vain ;  ye  are  yet  in  your  sins.  Then 
they  also  which  are  fallen  asleep  in  Christ  are  perished.  If  in 
this  life  only  we  -have  hope  in  Christ,  we  are  of  all  men  most 
miserable. — 1  Cor.  xv,  12— 19. 

58.  A  system  of  government  which  extends  to  those  actions  that  are 

performed  secretly  must  be  one  which  refers  either  to  a  regular 
divine  providence  in  this  life,  or  to  the  rewards  and  punish- 
ments of  another  world ; 
Every  perfect  system  of  government  must  extend  to  those  actions 

which  are  performed  secretly  ; 

.*.  JSFo  system  of  government  can  be  perfect  which  does  not  refer 
either  to  a  regular  divine  providence  in  this  life,  or  to  the  re- 
wards and  punishments  of  another  world. —  Wai-burton's  Divine 
Legation.  See  vi,  §  5. 

59.  There  are  two  kinds  of  things  we  ought  not  to  fret  about, — what 

we  can  help,  and  what  we  cannot.    (From  this,  form  a  dilemma.) 

60.  We  must  either  gratify  our  vicious  propensities  or  resist  them ; 

the  former  course  will  involve  us  iu  sin  and  misery,  the  latter 
requires  self-denial ;  therefore  we  must  either  fall  into  sin  and 
misery,  or  practise  self-denial. 


ANALYSIS    OF    CONDITIONALS.  225 


VI.  ANALYSIS  OF  CONDITIONALS. 

§  1.  A  categorical  proposition  declares  a  relation  between  two 
terms  unconditionally;  that  is,  no  condition  being  expressed.  A  con- 
ditional or  hypothetical  proposition  involves  an  express  condition. 
The  latter  is  a  complex  sentence,  consisting,  in  the  conjunctive  form, 
of  a  principal  clause,  the  apodosis  or  consequent,  and  of  a  subordinate 
clause,  the  protasis  or  antecedent  or  condition. 

The  question  whether  conditional  propositions  and  syllogisms  may 
or  may  not  be  reduced  to  categorical  forms  is  much  discussed  by 
logicians.  "By  Kant  and  his  followers  the  hypothetical  proposi- 
tion is  described  as  representing  a  form  of  judgment  essentially  dis- 
tinct from  the  categorical;  the  latter  being  thoroughly  assertorial, 
the  former  problematical  in  its  constituent  parts,  assertorial  only  as 
regards  the  relation  between  them.  Two  judgments,  each  in  itself 
false,  may  thus  be  hypothetically  combined  in  a  single  truth ;  and 
this  combination  cannot  be  reduced  into  categorical  form.  The  hypo- 
thetical syllogism,  in  like  manner,  is  a  form  of  reasoning  distinct  from 
the  categorical,  and  not  reducible  to  it,  being  based  on  a  different  law 
of  thought,  namely,  the  Logical  Principle  of  Sufficient  Reason,  a  ra- 
tione  ad  rationatum,  a  negatione  rationati  ad  negationem  rationis  valet 
consequential  J 

But  observe  that  the  question  is  not  properly  whether  the  categor- 
ical and  hypothetical  forms  are  convertible.  Logic  as  the  Theory  of 
Thought  has  no  concern  with  what  may  or  may  not  be  done  with 
forms.  The  question  proper  to  Logic  is  this :  Does  thought  hypo- 
thetically expressed  differ  from  that  categorically  expressed ;  and  if  so, 
what  is  the  specific  difference  ?  In  other  words,  Are  there  two  proc- 
esses of  thought,  as  there  are  two  kinds  of  propositions,  and  do  we 
need  a  distinct  system  of  syllogizing  to  explain  how  we  necessarily 
think  when  matter  is  thought  hypothetically  ?  We  propose  now  to 
show  that  while  there  are  two  spheres  of  thought,  its  process  is  one ; 
that  all  reasoning  has  essentially  the  same  form,  having  the  Aristotelic 
syllogism  for  its  formal  unit.  We  propose  to  discover  the  true  rela- 

i  See  Kant's  Log'ik,  §  25  and  §  76  ;  and  Hansel's  Aldrich,  Appendix,  Note  I. 

15 


226  OF    REASONINGS. 

lions  of  categorical  and  hypothetical  thinking,  and  to  show  that  they 
do  not  differ  logically,  but  only  psychologically. 

In  attempting  this,  we  will  first  point  out  a  psychological  distinc- 
tion between  two  spheres  of  thought ;  then  consider  the  propositional 
use  of  hypotheticals,  and  the  syllogisms  arising  therefrom  ;  and  then 
advert  to  the  common  logical  doctrine  of  conditionals.  Herein  we 
hope  to  confirm  the  general  doctrine  of  this  Treatise,  that  thought 
is  of  only  two  logical  kinds,  immediate  and  mediate,  and  that  of  the 
latter  the  Aristotelic  syllogism  is  ultimately  the  universal  form. 

§  2.  Thought  is  either  of  the  real  or  of  the  ideal.  Real  thought 
considers  its  matter  as  existent,  and  affirms  or  denies  of  it  categorically. 
Ideal  thought  considers  its  matter  as  merely  logically  possible,  and  af- 
firms hypothetically,  that  is,  in  a  supposititious  mode.  This  matter 
may  or  may  not  really  exist ;  but  thought  posits  merely  its  ideal  exist- 
ence, and,  limited  only  by  self-contradiction,  proceeds  to  evolve  logi- 
cally conceivable  consequences.  So  even  when  the  matter  is  known 
to  be  real,  the  mind  may  choose  rather  to  view  it  ideally,  thought 
readily  transferring  it  from  one  sphere  to  the  other.  Thus  when  I  say 

Plato  is  a  man,  therefore  he  is  mortal, 

I  think  the  matter  real,  and  draw  a  real  conclusion.     But  when  I  say 
If  Plato  be  a  man,  then  he  is  mortal, 

I  think  the  matter  ideally,  making  a  supposition  without  regard  to 
fact,  and  on  this  hypothetical  statement  I  reason  to  an  equally  ideal 
conclusion. 

What  distinguishes  ideal  from  real  thought  is  precisely  what  dis- 
tinguishes hypothetical  from  categorical  judgments.  Thus  far  we 
have  used  the  words  "conditional"  and  "hypothetical"  as  inter- 
changeably synonymous.  But  the  former  is  opposed  to  "  categorical " 
in  the  characteristic  that  it  formally  expresses  a  condition  of  the 
principal  thought;  the  latter  in  the  other  characteristic  that  it  ex- 
presses ideal,  supposititious  thought,  and  not  real  declared  fact.  The 
words  should  be  used  accordingly. 

It  is  manifest  that  the  distinction  between  categorical  and  hypo- 
thetical judgments  as  real  and  ideal  is  not  logical,  but  psychological. 
This  will  still  more  plainly  appear  when  it  is  shown  that  thought  in 
the  real  and  in  the  ideal  sphere  is  logically  the  same ;  that  is,  governed 
by  the  same  laws,  assuming  the  same  forms,  analyzing  into  the  same 
principles,  and  hence  indistinguishable  on  logical  grounds. 


ANALYSIS    OF    CONDITIONALS.  227 

These  two  mental -moods,  the  real  and  the  ideal,  are  formally  ex- 
pressed by  the  two  grammatical  moods,  indicative  and  subjunctive. 
It  would  seem  that  by  a  language  scientifically  constructed  and  ex- 
pressing accurately  the  mind  of  the  speaker,  these  moods  would  always 
be  sharply  discriminated.  But  perhaps  in  all  of  the  more  refined 
languages,  notably  in  our  own,  there  has  been  a  strong  tendency  to 
obliterate  the  subjunctive  forms,  and  to  substitute  the  indicative  to 
express  ideal  thought.  In  hypothetical  propositions,  which  are  all 
essentially  ideal,  the  indicative  has  largely  usurped  the  place  of  the 
subjunctive. 

It  is  quite  common  for  grammarians  to  characterize  the  subjunctive 
mood  as  expressive  of  doubt  or  uncertainty.  But  this  is  inept,  for  its 
past  tenses  never  express  doubt,  and  its  present  tense  is  entirely  con- 
sistent with  full  conviction,  the  doubt  in  this  case,  so  far  as  the  ex- 
pression implies  it,  being  altogether  formal  or  rhetorical,  and  not 
actual.  It  should  be  observed  that  the  real  and  ideal  arc  modes  of 
cognition,  of  intellectual  apprehension ;  whereas  belief  and  doubt  are 
feelings,  modes  of  self-consciousness.  These  coexist  with  cognitions, 
but  are  very  widely  separated  from  them  in  psychological  analysis. 
If,  then,  they  are  not  to  be  made  the  basis  of  a  psychological  distinc- 
tion between  modes  of  thought,  much  less  should  they  be  made  the 
basis  of  a  logical  distinction.  Any  uncertainty  attending  a  premise 
modifies  in  no  way  whatever  the  character  of  our  reasoning.  We  do 
not  reason  one  way  when  we  are  in  doubt,  and  in  another  when  we 
are  certain.  In  all  cases  reasoning  proceeds  apodeictically,  the  deduc- 
tion is  necessary,  not  more  so  in  demonstration  than  in  dialectics. 
An  uncertainty  in  a  premise  is  carried  along,  and  attaches  to  the  con- 
clusion, without  being  itself  increased  or  diminished.  The  doubt  af- 
fects not  the  reasoning,  nor  the  reasoning  the  doubt.  Hence  we  must 
here  set  entirely  aside  any  consideration  of  the  feelings  of  certainty, 
degree  of  belief,  doubt,  etc. ;  and  especially  have  care  not  to  confuse 
these  feelings  with  the  intellectual  moods  real  and  ideal. 

The  indicative  mood,  then,  properly  deals  with  the  real.  It  de- 
clares concerning  facts  as  facts.  It  has  moreover,  perhaps  under  the 
influence  of  doubt,  taken  upon  itself  to  express,  what  properly  belongs 
to  the  subjunctive,  ideal  thought.  The  present  subjunctive  deals  with 
a  subjective  ideal  which  is  objectively  contingent.  It  expresses  a  sup- 
position of  a  fact, — the  ideal ;  one  which  may  or  may  not  become  a 
fact, — the  contingent.  The  past  tenses  of  this  mood  have,  in  usus  lo- 
quendij  come  to  express  a  supposition  contrary  to  fact, — an  ideal,  not 


228  OF    REASONINGS. 

contingent,  but  unreal.     The  psychological  distinction  between  real 
and  ideal  thought  is  thus  profoundly  embedded  in  language.3 

It  will  be  useful  to  illustrate  this  matter  by  some  divisions,  taken 
in  a  grammatical  rather  than  a  logical  view.  In  the  development  of 
our  language,  the  tenses  of  the  subjunctive  have  moved  forward  in 
time,  so  that  usually  the  present  tense  expresses  future  time ;  the  im- 
perfect tense,  present  time,  etc.  The  present  tense  has  not,  however, 
ceased  to  express  present  time.  E.  g.,  "If  the  book  be  in  this  room, 
it  may  be  found."  Perhaps  more  commonly  now  it  would  be  said, 
"  If  the  book  is  in  this  room,"  etc.,  which,  though  indicative,  is  equally 
ideal  and  contingent.  Considering,  however,  the  step  forward  in  time 
as  established,  we  find  three  phrases  of  ideal  subjunctive  thought : 
1st.  The  ideal  and  contingent  future;  both  the  protasis  and  apodosis 
being  suppositions  lying  in  the  future ; 

(a)  Future  from  the  standpoint  of  the  present ;  e.  g. : 

If  he  repent,  he  should  be  forgiven. 
Should  he  come,  he  would  be  welcome. 
Only  were  you  to  wax  fat,  should  I  love  you  more. 
I  tell  you  that,  if  these  should  hold  their  peace, 
the  stones  would  immediately  cry  out. 

(b)  Future  from  the  standpoint  of  the  past ;  e.  g. : 

I  told  you  if  you  were  to  do  this,  I  would  reward  it. 

2d.  The  ideal  and  unreal  present ;  it  being  implied  that  neither  the 
protasis  nor  apodosis  really  exists ;  e.  g. : 

If  he  were  here,  I  would  tell  him.     I  would  if  I  could. 
Were  the  question  definite,  it  should  be  answered. 
The  moon  would  be  always  full  if  it  were  self-luminous. 

If  all  the  year  were  playing  holidays, 

To  play  would  be  as  tedious  as  to  work. — Shakespeare. 

3d.  The  ideal  and  unreal  past ;  wherein  likewise  the  real  existence  of 
both  protasis  and  apodosis  is  impliedly  denied ;  e.  g. : 
If  he  had  been  present,  I  should  have  seen  him. 
Could  the  fort  have  held  out,  the  city  would  not  have  been  taken. 

Oh,  had  your  fate  been  joined  with  mine, 

As  once  this  pledge  appeared  the  token ; 
These  follies  had  not  then  been  mine, 

My  early  vows  had  not  been  broken. — Byron, 

2  Too  deeply  to  be  uprooted  or  disturbed  by  Schelling's  Philosophy  of  Identity, 
declaring  the  absolute  identity  of  the  real  and  the  ideal,  of  being  and  thinking. 


ANALYSIS    OF    CONDITIONALS.  229 

Besides  these  fundamental  forms  of  the  pure  and  strict  subjunctive, 
there  are  a  number  of  mixed  forms,  as  follows : 

Past  tense  combined  with  the  present ;  e.  g. : 

Had  he  been  prudent,  he  were  now  living. 

Were  these  his  companions  prudent,  he  had  not  lost  his  life. 

Subjunctive  protasis  with  indicative  apodosis ;  e.  g. : 

If  this  be  judged  treason,  still  will  I  maintain  it. 
The  same  in  the  concessive  relation  (see  v,  §  9,  Ex.  17) ;  e.  g. : 

Though  hand  join  in  hand,  the  wicked  shall  not  be  unpunished. 
The  same  in  the  iterative  relation,  equivalent  to  a  general  rule ;  e.  g. : 

If  (at  any  time,  or  whenever)  the  centres  of  the  sun  and  moon  be  in  the 
same  line  with  the  centre  of  the  earth,  there  must  be  an  eclipse. 

The  subjunctive  with  the  imperative ;  e.  g. : 

If  love  be  rough  with  you,  be  rough  with  love. — Shakespeare. 

If  thou  be  the  Son  of  God,  command  that  these  stones  be  made  bread. 

The  subjunctive  with  the  potential ;  e.  g. : 

Had  you  seen  {he  city  before  it  was  razed,  you  might  have  thought  it  in- 
destructible, and  could  not  have  foreseen  its  fate. 

A  comparative  construction  with  an  ellipsis  of  the  apodosis ;  e.  g. : 
He  brags  as  (he  would  brag]  if  he  were  of  note. — Shakespeare. 

Any  special  examination  of  these  mixed  forms  must  be  omitted ;  we 
only  observe  that,  being  mixed,  the  principles  governing  their  elements 
govern  them. 

§  3.  The  conjunctive  hypothetical,  then,  is  an  ideal  form  of  speech 
expressing  either  the  contingent  or  the  unreal.  The  protasis  is  a  sub- 
ordinate clause  related  to  the  apodosis,  in  the  contingent  forms,  either 
as  a  qualifier  or  as  an  antecedent  condition.  This  indicates  a  double 
use  that  is  made  of  these  hypothetical  forms  in  thought.  They  are 
either  propositions  containing  a  qualified  term,  or  they  are  propo- 
sitions declaring  an  inference.  We  will  first  consider  the  qualified 
propositions. 

Looking  on  the  contingent  forms,  we  observe  that  very  often  the 
sole  purpose  in  the  mind  of  a  speaker  using  this  form  is  to  declare  an 
ideal  truth.  It  is  a  mere  proposition,  one  not  intended  to  offer  a 
reason,  but  to  state  a  judgment.  In  such  case,  since  the  mind  passes 
readily  from  the  ideal  sphere  to  the  real,  and  vice  versa,  these  prop- 


230  OF    REASONINGS. 

ositions  may  generally  be  easily  reduced  to  categorical  forms.  The 
protasis  being  viewed,  not  as  a  condition,  but  rather  as  a  qualification, 
explicative  or  limitative,  we  may  redress  the  four  forms  (v,  §  2)  thus : 

1  (a)  If  a  house  be  undermined,  it  will  fall ; 
i.  e.,  A  house  undermined  will  fall. 

(b)  If  virtue  is  voluntary,  vigor  is  not  a  virtue  ; 

i.  e.,  Vigor  is  not  voluntary  virtue. 

(c)  If  mere  rhyming  is  poetry,  poetry  is  easily  written ; 

i.  e.,  Poetry  that  is  mere  rhyming  is  easily  written. 

(d)  If  carbon  will  burn,  the  diamond  will  burn ; 

i.  e.,  The  diamond,  being  carbon,  will  burn. 

What  the  hypothetical  here  states  ideally,  the  categorical  equivalent 
states  as  a  real  fact.  This  difference  is  psychological  and  grammati- 
cal, not  logical.  The  hypothetical  proposition  is  grammatically  a 
complex,  but  logically  a  simple,  sentence.  The  generality  of  a  uni- 
versal statement  must  not  be  confused  with  the  ideality  of  a  hypo- 
thetical. When  we  say  "  A  house  undermined  will  fall,"  and  "  An  in- 
jurious deed,  if  it  be  unintentionally  committed,  is  not  a  crime,"  the 
former  is  stated  as  a  real  fact,  having  a  potential,  if  not  an  actual,  ex- 
istence. It  is  general,  not  ideal.  The  latter  is  both  general  and  ideal. 

Each  of  the  foregoing  examples  may  be  taken  as  a  general  rule,  and 
stand  as  the  major  premise  of  a  syllogism,  or  it  may  be  viewed  as  a 
specialized  statement,  and  used  as  a  minor.  Other  cases  are  some- 
times only  particular,  and  fitted  to  become  only  minors.  The  follow- 
ing, cited  by  Fries3  as  an  example  of  a  hypothetical  not  reducible  to 
categorical  form,  is  general  or  particular  according  as  we  interpret  it : 

If  Caius  is  disengaged,  he  is  writing  poetry. 
It  may  be  construed  as  a  universal  statement  meaning — 
Caius,  whenever  disengaged,  is  writing  poetry, 

thus  expressing  iterative  relation,  "  At  any  or  every  time  that,"  etc. 
But  it  may  also  be  construed  as  a  particular  statement  meaning — 
Caius,  being  disengaged,  is  now  writing  poetry. 

3  System  der  Logik,  §  62.  "  Es  ist  sogar  f ehlerhaf t,  indem  man  behauptet,  in  jeder 
hypothetischen  Regel,  die  nur  ein  Subjekt  hat,  konne  man  die  beiden  Pradikate  in 
eine  kategorische  Regel  verbinden ;  z.  B.,  '  Wenn  Caius  frei  von  Geschaften  ist, 
so  dichtet  er.'  Im  Allgemeinen,  wenn  der  ganze  Yordersatz  oder  sein  Subjekt 
mit  dem  Pradikat  verbunden  und  nicht  nur  sein  Pradikat  der  Grund  im  Satze  ist, 
so  geht  diese  Veranderung  gar  nicht.  Noch  willkiirlicher  sind  die  Veriinderungen, 
wenn  die  hypothetische  Regel  zwei  verschiedene  Subjekte  hat."  See  also  Man- 
gel's Aldr'wli,  p.  239. 


ANALYSIS    OF    CONDITIONALS.  231 

To  illustrate  various  expression,  one  other  example  of  this  transfer- 
ence from  the  ideal  to  the  real  will  suffice : 

Were  he  to  repent,  he  would  be  forgiven. 

The  apodosis  is  affirmed  in  case  that  the  contingency  expressed  by  the 
protasis  become  a  fact.  The  whole  is  an  ideal  lying  in  the  future.4 
Transforming  the  proposition,  the  ideal  becomes  real,  the  affirmation 
categorical :  He>  repenting,  will  be  forgiven. 

These  considerations  recall  a  remark  formerly  made  that  an  adjec- 
tive word,  phrase,  or  clause  is  the  result  of  a  previous  judgment. 
We  shall  find  hereafter  that  in  the  hypothetical  proposition  viewed 
as  an  inference,  it  is  the  middle  term  that  becomes  the  adjective  qual- 
ifier.    Hence  every  categorical  proposition  having  a  qualified  subject 
may  be  easily  converted  into  an  ideal  statement ;  as  follows: 
A  soft  answer  turneth  away  wrath. 
If  an  answer  be  soft,  it  turneth  away  wrath. 

The  examples  so  far  contain  only  three  terms.     Because  they  are 
reducible  to  simple  categoricals,  therefore,  says  Thomson,  they  are 
not  true  hypotheticals ;  the  proposition  of  four  terms,  since  it  cannot 
be  so  reduced,  is  the  true  hypothetical.     But  let  us  test  this : 
If  the  wise  are  virtuous,  Socrates  was  innocent ; 

i.  e.,  The  wise  Socrates,  who  was  virtuous,  was  innocent. 
If  a  government  is  well  administered,  the  people  are  prosperous ; 
i.  e.,  If  a  government  is  well  administered,  it  has  prosperous  people ; 
i.  e.,  A  well-administered  government  has  prosperous  people. 
If  there  are  spots  on  the  sun,  the  needle  is  disturbed ; 

i.  e.,  The  needle  is  disturbed  whenever  there  arc  spots  on  the  sun. 

That  in  some  cases  it  is  difficult,  or  even  impracticable,  to  make  such 
reduction  is  only  because  some  connecting  media,  not  contained  in  the 

4  Let  us  note  that  the  event  of  his  repenting,  being  contingent,  is  doubtful,  but 
not  that  he  would  in  that  case  be  forgiven.  This  may  be  said  of  Satan  himself ; 
but  then  the  doubt  could  hardly  exist,  for  we  feel  quite  sure  he  will  never  repent, 
and  hence,  on  that  ground,  will  never  be  forgiven, — a  near  approach  to  the  unreal 
statement.  Burns,  however,  with  bizarre  tenderness,  felt,  or  affected  to  feel,  oth- 
erwise, doubting  also  the  forgiveness  even  in  the  event  of  repentance : 

"  But  fare  you  weel,  auld  Nickie-ben  ! 
Oh  wad  ye  tak  a  thought,  an'  men', 
Ye  aiblins  might — I  dinna  ken — 

Still  hae  a  stake — 
I'm  wae  to  think  upo'  your  den, 

Ev'n  for  your  sake !" 


232  OF    REASONINGS. 

proposition,  are  obscure  or  unknown.  But  this  does  not  differentiate 
these  propositions  as  of  another  kind.  Nor  is  it,  as  Thomson  says, 
that  conjunctives  of  four  terms  arc  always  causal.  Attributives  of 
four  terms,  as  the  first  example  above,  are  very  common,  as  well  as 
reducible  causals  of  three  terms.  Moreover,  there  is  no  reason  why, 
in  deductive  Logic,  the  causal  should  be  distinguished  from  the  at- 
tributive judgment.  In  logical  deduction  all  judgments  are  thought 
attributively,  and  cause  and  effect,  so  far  as  they  are  conceived  in 
thought,  stand  to  each  other  in  the  relation  of  reason  and  consequent. 
Objective  cause  becomes  subjective  reason. 

§  4.  Let  us  consider  now  the  contingent  forms  as  propositions  de- 
claring an  inference.  The  conjunctive  proposition,  as  a  whole,  affirms 
a  relation  between  the  two  subordinate  propositions  of  which  it  con- 
sists. It  expresses  a  judgment  respecting  judgments.  It  is  logically 
a  simple  sentence.  The  apodosis  is  the  subject,  and  the  protasis  the 
predicate.5  The  protasis  (jrpoTtiveiv}  is  so  named,  and  usually  writ- 
ten first,  because,  as  we  shall  hereafter  show,  it  is  in  reality  a  premise, 
and  hence  the  logical  antecedent. 

And  what  is  the  relation  the  conjunctive  declares  ?  This  relation  is 
invariable.  It  is  the  relation  of  consequence.  The  proposition  declares 
that  one  judgment  is  consequent  on,  or  follows  from,  another.  Let 
it  now  be  particularly  observed  that  the  affirmation  is  not  only  simple, 
but  categorical;  1.  c.,  this  relation  is  affirmed  unconditionally.  E.  g. : 

If  virtue  is  knowledge,  it  is  teachable. 

Now  strip  this  proposition  of  its  hypothetical  dress,  and  we  have — 
That  virtue  is  teachable  is  an  inference  from  the  judgment  that  it  is  knowledge. 

This  is  purely  categorical.  But  not  less  is  it  categorical  when  pre- 
sented in  its  hypothetical  dress.  The  relation  of  the  clauses  is  real. 

5  The  logicians  generally  invert  this  statement.  But  the  subject,  properly,  is 
that  of  which  something  is  said,  which  evidently  here  is  the  apodosis ;  e.  g. : 

If  history  is  reliable,  the  latter  days  are  the  better  days. 

Here  we  are  talking  about  the  latter  days  being  the  better  days,  and  we  say  quite 
simply  that  its  truth  is  conditioned  on,  or  follows  from,  the  reliability  of  history. 
This  relation  of  subject  and  predicate  in  conjunctives  would  be  a  little  plainer  if 
the  usual  form  were,  as  in  the  present  sentence,  inverted,  and  stated  thus : 

C  is  D,  if  A  is  B  ; 
The  flowers  will  bloom,  if  the  sun  shines. 


ANALYSIS    OF    CONDITIONALS.  233 

That  the  conjunctive  proposition,  having  one  clause  as  its  subject, 
the  other  as  predicate,  and  declaring  the  relation  of  consequence,  is  a 
simple  categorical  will  perhaps  be  a  little  clearer  if  we  look  into  the 
matter  of  the  proposition,  and  consider  wherein  lies  its  material  truth 
or  falsity.  When  we  say 

If  man  is  responsible,  he  must  be  a  free  agent, 

we  do  not  affirm  the  reality  of  his  responsibility  nor  of  his  free  agency. 
These  are  treated  here  as  ideal.  But  we  do  affirm  the  real  connection, 
the  necessary  coexistence  of  the  two.  Indeed,  the  force  of  the  word 
"  must "  in  the  example  is  to  declare  the  necessity  of  this  consequence. 
That  the  conjunction  of  the  two  clauses,  the  dependence  of  one  on 
the  other,  is  all  that  is  affirmed  is  still  more  manifest  when  we  con- 
sider that  the  truth  of  this  affirmation  is  entirely  independent  of  the 
truth  of  the  clauses.  E.  g. : 

If  the  Koran  came  from  God,  Mohammed  was  the  prophet  of  God. 

The  truth  of  this  statement  is  indisputable,  yet  we  hold  both  of  the 
clauses,  considered  apart,  to  be  false. 

A  false  hypothetical  is  said  to  be  one  having  a  false  condition. 
This,  however,  does  not  mean  that  the  protasis  is  false,  but  that  the 
affirmation  of  consequence  is  false,  that  the  given  condition  is  not  the 
condition.  Hence  it  would  perhaps  be  better  to  say  that  a  false  hypo- 
thetical is  one  affirming  as  consequent  what  is  inconsequent.  E.  g. : 

If  Moses  was  a  lawgiver,  he  was  very  meek. 

Here  we  may  admit  each  clause  separately  to  be  true,  but  the  propo- 
sition as  a  judgment  respecting  judgments  is  false ;  the  one  does  not 
follow  from  the  other.  The  concessive  clause,  granting  a  protasis,  de- 
nies the  consequence,  thus  pronouncing  the  hypothetical  false ;  but  it 
does  more,  it  denies  the  apodosis  also.  E.  g. : 

(If  our  outward  man  perish,  the  inward  man  must  fail.) 

"  Though  our  outward  man  perish,  the  inward  man  is  renewed." 

Since,  then,  the  truth  and  acceptance  of  a  conjunctive  proposition 
lie  wholly  in  the  correctness  of  this  single  unconditional  declaration 
of  sequence,  it  is  manifest  that  the  statement,  as  a  whole,  is  a  simple 
categorical  affirmation  of  this  relation. 

In  the  previous  section  it  appeared  that  the  conjunctive  hypothet- 
ical in  its  first  prepositional  use  makes  simply  an  ideal  statement,  and 
that  the  sole  difference  in  thought  between  it  and  the  correspond- 


234  OF    REASONINGS. 

ing  categorical  judgment  is  that  the  former  is  ideal,  the  latter  real; 
a  difference  that  is  non-logical.  It  now  appears  that  the  same  hypo- 
thetical in  its  second  prepositional  use,  as  declaring  the  relation  of 
inference,  is,  in  that  regard,  categorical  and  real.  In  a  former  chapter 
it  was  pointed  out  that  the  syllogistic  judgment  in  the  categorical  or 
Aristotelic  syllogism  simply  and  solely  declares  consequence.  Where- 
in then  is  the  distinction  between  this  and  the  hypothetical  expres- 
sion of  inference  ?  None  appears  beyond  this,  that  in  the  syllogistic 
judgment  the  inference  is  from  matter  that  is  pronounced  real,  where- 
as in  the  hypothetical  judgment  the  inference  is  from  matter  that  is 
ideal.  This  difference,  we  repeat,  is  psychological,  not  logical.  So 
far,  then,  we  find  no  ground  to  justify  a  logical  discrimination  between 
categorical  and  hypothetical  thought.6 

Before  advancing  in  our  analysis,  two  remarks  arc  worthy  of  place. 
First:  We  have  pointed  out  the  subject  and  predicate  of  the  conjunctive ; 
where  is  the  copula?  Many  logicians  call  the  conjoining  particle, 
united  with  the  verb  "  to  be"  the  copula.  Thus,  say  they,  in  con- 
junctives it  takes,  among  others,  these  forms :  "  If then  is ;" 

"  When  -  -  then  is ;"  "  Where  -  -  there  is ."  In  dis- 
junctives these  forms :  "  Either  is or  is ;"  " is  either 

or ."  This  is  a  confusing,  and  in  Logic  an  improper,  use  of 

the  word  "  copula."  Let  us  rather  say  that  the  appearance  of  the 
copula  in  the  conditional  forms  is  grammatically  inadmissible,  but 
that  it  is  implied  by  the  conjunctive  and  disjunctive  and  illative 
particles.7 

We  remark,  secondly,  that  while  the  common  characteristic  of 
the  conjunctive  and  syllogistic  judgments  is,  as  above  indicated,  the 
affirmation  of  the  sequence  of  dependence,  it  is  not  at  all  peculiar  to 

6  It  may  be  well  to  note  that  immediate  inferences  are  easily  expressed  ideally; 
e.  g.,  "  If  ignorance  is  degrading,  then  something  that  degrades  is  ignorance."   This 
is  merely  conversion  per  accidens. 

7  The  word  "«/","  which  is  the  most  usual  grammatical  characteristic  of  the  con- 
junctive, is  classed  as  a  conjunction.     But  it  was  originally  a  transitive  verb,  hav- 
ing for  its  object  the  clause  following  it.    As  explained  by  Home  Tooke,  in  Diver- 
sions of  Parley,  it  is  the  Anglo-Saxon  gif,  the  imperative,  second  person  singular,  of 
the  verb  gif  an,  to  give.     Its  original  meaning,  then,  is  "  grant,"  "  allow,"  "  admit," 
"suppose,"  but  is  now  equivalent  to  "provided  that,"  "in  case  that,"  "should  it 
be  proved  that,"  or  "  it  follows  from that."     Thus : 

If  a  man  love  me,  he  will  keep  my  words. 
That  is,  grant  this  premise,  and  the  conclusion  must  follow. 


ANALYSIS    OF    CONDITIONALS.  235 

them  to  be  propositions  respecting  propositions.  Like  other  things, 
propositions  have  a  variety  of  attributes.  In  a  conjunctive  the  attri- 
bute predicated  is  that  of  being  an  inference  from  another  proposition. 
But  this  is  only  one  of  many  attributes  that  may  be  predicated.  E.  g. : 

That  the  whole  is  greater  than  a  part  is  a  mathematical  axiom. 

My  belief  is  that  with  God  time  is  an  eternal  now. 

It  is  obvious  that  propositions  may  be  either  term  of  a  predication. 

§  5.  "When  in  thought  we  use  the  protasis  merely  as  a  qualifier  of  a 
term  of  the  apodosis,  it  is  quite  evident  that  we  may  reason  from  such 
judgments  as  premises  whether  reduced  to  categorical  form  or  not. 
The  only  difference  is,  that  when  the  judgments  are  in  hypothetical 
form,  we  are  then  reasoning  in  the  ideal  mood;  when  reduced  to  cate- 
goricals,  we  think  the  matter  as  real.  "When,  on  the  other  hand,  we 
view  the  propositions  as  declaring  an  inference,  we  may  likewise  rea- 
son from  them  as  premises,  and  this  judgment  being  categorical,  its 
matter  is  real.  We  may  understand  "  ?/"  as  representing  the  copula 
"follows from"  and  present  a  typical  form,  thus: 

C  is  D  if  A  is  B ; 

E  is  F  if  C  is  D ; 

.'.  E  is  F  if  A  is  B. 

The  order  of  nature  is  the  product  of  benevolent  design, 

if  it  tends  to  promote  moral  good ; 
It  must  have  had  an  intelligent  and  beneficent  author, 

if  it  is  the  product  of  benevolent  design ; 
.*.  It  must  have  had  an  intelligent  and  beneficent  author, 
if  it  tends  to  promote  moral  good. 

This,  evidently,  is  Barbara.  Returning  to  the  usual  form,  the  follow- 
ing example  is  only  in  part  hypothetical : 

If  the  using  of  credit  is  a  demand  for  goods, 

all  forms  of  credit  affect  prices ; 
But  bills  of  exchange  are  a  form  of  credit ; 
.'.  If  the  using  of  credit  is  a  demand  for  goods, 

bills  of  exchange  affect  prices. 

This,  also,  is  Barbara.  We  call  attention  to  its  easy  solution  by  the 
Canon  of  Replacement. 

It  is  manifest,  then,  that,  so  far,  we  discover  no  new  principles,  and 
hence  need  no  new  rules  or  forms.  These  examples  may  properly  be 
called  Conjunctive  Hypothetical  Syllogisms,  and  so  distinguished  from 


236  OF    REASONINGS. 

the  purely  categorical  forms ;  but  the  difference  is  evidently  not  a 
logical  difference. 

Let  us  at  once  extend  the  view  to  other  forms  of  hypothetical. 
The  disjunctive  proposition,  which,  as  we  shall  hereafter  show,  is  com- 
pounded of  conjunctives,  and  therefore  subject  to  the  same  treat- 
ment, may,  however,  be  considered  as  a  simple  categorical  affirmation, 
either  predicating  alternatives,  or  predicating  a  mark  of  alternatives. 
So,  then,  we  may  have  Aristotelic  syllogisms  formed  of  disjunctives, 
and  such  are  true  Disjunctive  Hypothetical  Syllogisms.  E.  g. : 

Memory  is  either  circumstantial  or  philosophic ; 
Also  it  is  either  voluntary  or  spontaneous ; 
.*.  In  this  case,  what  is  either  voluntary  or  spontaneous 
is  also  either  circumstantial  or  philosophic. 

This  is  Darapti.  The  following  consists  partly  of  disjunctives.  It  is 
evidently  Aristotelic ;  but  its  reduction  to  strict  logical  form,  thus  de- 
termining its  mood,  is  quite  a  complex  process.  Its  solution  by  re- 
placement is,  however,  obvious  and  easy  : 

Desires  are  either  spontaneous  or  voluntary ; 
But  whatever  is  voluntary  has  moral  quality ; 
.*.  Desires  are  either  spontaneous,  or  they  have  moral  quality. 

Since  the  Dilemmatic  proposition  is  a  compound,  a  conjunctivo-dis- 
junctive,  it  is  subject  to  the  same  view,  and  we  may  have  Aristotelic 
syllogisms  involving  it.  E.  g. : 

If  a  ruler  makes  an  entirely  unselfish  use  of  despotic  power, 

he  must  be  cither  a  saint  or  a  philosopher; 
But  saints  and  philosophers  are  rare ; 
.'.  Those  rulers  who  so  conduct  themselves  are  rare. 

There  are,  of  course,  Enthymemes,  comprising  hypotheticals.     E.  g. : 

If  matter  is  essentially  inert,  there  must  be  a  higher 
moving  power,  and  this  implies  a  governing  will. 

So,  also,  we  may  have  Epichiremas,  comprising  hypotheticals.     E.  g. : 

If  government  has  a  right  to  enforce  the  laws, 

and  without  this  it  could  not  subsist, 

then  it  has  a  right  to  use  military  force  against  its  own  citizens, 

for  in  extreme  cases  this  may  be  requisite ; 
If  so,  then  government  has  a  right  to  inaugurate  civil  war, 

since  civil  war  is  the  likely  result  of  such  use 

of  military  power,  counter  to  the  right  of  revolution ; 
/.  If  a  state  has  a  right  to  enforce  its  laws, 

it  has  the  right  to  inaugurate  civil  war 

for  the  suppression  of  revolution. 


ANALYSIS    OF    CONDITIONALS.  237 

A  series  of  hypothetical  syllogisms  formed  of  conditional  proposi- 
tions may  be  abridged  into  a  Sorites.  E.  g. : 

If  the  Scriptures  are  the  word  of  God,  they  should  be  clearly  explained ; 
If  they  should  be  clearly  explained,  they  must  be  diligently  studied ; 
If  they  must  be  diligently  studied,  an  order  of  men  must  be  devoted  to  them  ; 
.*.  If  the  Scriptures  are  the  word  of  God,  an  order  of  men  must  be  devoted  to  them. 

This  is  purely  Aristotelic  reasoning.     Had  we  affirmed — 

But  the  Scriptures  are  the  word  of  God ; 
.'.  An  order  of  men  must  be  devoted  to  them — 

the  forms  would  be  mixed,  the  last  step  being  the  so-called  hypothet- 
ical syllogism,  in  the  ponent  mood.  Finally,  we  may  construct  a 
Sorites  consisting  of  disjunctives,  wherein  the  reasoning  is  strictly 
Aristotelic.  The  following  is  partly  of  this  character,  and  involves  a 
prosyllogism : 

•  Every  science  is  either  pure  or  inductive ; 
A  pure  science,  since  it  treats  of  the  necessary  forms 
either  of  thought  or  of  imagination, 
is  either  logical  or  mathematical ; 
A  mathematical  science  is  either  exact  or  worthless ; 
The  science  of  probabilities  is  neither  logical  nor  exact ; 
.*.  It  is  either  inductive  or  worthless. 

The  reasoning  in  all  these  cases  turns  upon  the  categorical  affirma- 
tion of  sequence  alone.  Hence  it  is  strictly  of  Aristotelic  form,  comes 
under  its  moods,  and  is  subject  to  its  Canon  and  rules.  Logic,  then, 
cannot  distinguish  these  as  kinds  of  reasoning,  as  different  forms  of 
thought. 

§  6.  But  the  conjunctive  proposition,  viewed  as  declaring  an  infer- 
ence, implies  within  itself  a  reasoning.  The  affirmation  of  sequence 
is  a  characteristic  common  to  it  and  the  syllogistic  judgment.  The 
protasis  is  a  condition  or  logical  antecedent  of  the  apodosis ;  in  other 
words,  it  is  a  premise,  and  the  apodosis  is  a  consequent,  or  conclusion. 

Now,  whether  a  conjunctive  is  thought  thus,  or  merely  as  a  quali- 
fied proposition,  can,  in  general,  be  ascertained  only  by  considering  the 
matter  and  the  context.  In  pure  Logic  it  is,  of  course,  undetermined. 
Let  us  illustrate : 

If  air  is  pure,  it  is  wholesome. 

This,  probably,  in  the  minds  of  most  persons  who  do  not  receive  it 
upon  mere  testimony,  is  a  direct  induction  from  observation  or  ex- 


238  OF    REASONINGS. 

perience,  and,  though  capable  of  being  construed  syllogistically,  is 
with  them  a  simple  judgment,  not  expressive  of  any  reasoning  what- 
ever, but  equipollent  with — 

Pure  air  is  wholesome. 
But  in  this  example, 

If  the  moon  has  no  atmosphere,  it  has  no  twilight, 

there  would  seem  to  be  a  reasoning  implied ;  the  apodosis  being  ne- 
cessitated by  the  protasis  standing  under  some  general  rule,  such  as : 

Atmosphere  is  essential  to  the  phenomenon  of  twilight. 
The  reasoning  thus  implied  may  be  expressed  in  full  as  follows : 

(An  orb  that  has  no  atmosphere  has  no  twilight ;) 
now,  If  the  moon  has  no  atmosphere, 

it  follows  that  The  moon  has  no  twilight. 

We  have,  then,  in  this  given  condition  or  protasis  an  ideal  minor 
premise,  yielding  an  ideal  conclusion,  the  apodosis.  It  is  manifest, 
therefore,  that  the  contingent  conjunctive  hypothetical  proposition 
declaring  an  inference  is  a  simple  Ideal  Enthymeme.8 

It  has  already  been  indicated  that  we  may  reason  in  the  ideal  sphere 
of  thought  as  well  as  in  the  real,  and  that  the  principles  are  precisely 
the  same.  We  may  pass  from  the  one  to  the  other;  from  the  real 
to  the  ideal  in  every  case;  from  the  ideal  to  the  real,  if  we  have 
ground.  In  the  last  example  we  have  a  major  real,  and  pass  to  an 
ideal  minor  and  conclusion.  We  may  readily  transfer  a  reasoning  to- 
tally from  the  real  to  the  ideal.  Thus,  it  is  easy  and  proper  to  say 

If  all  men  are  mortal, 
and    If  Plato  is  a  man, 
then  Plato  is  mortal. 

This  throughout  all  of  its  propositions  is  purely  ideal. 

8  A  varied  but  quite  correct  view  of  the  conjunctive  hypothetical  is  as  follows : 
It  is  merely  an  affirmation  of  necessary  sequence.  But  upon  what  does  this  se- 
quence depend?  Upon  the  existence  (in  the  Form  1  a)  of  an  unexpressed  major, 
under  which,  as  a  general  rule,  the  ideal  minor  would  come  as  a  special  case.  To 
affirm  the  sequence  is  only  to  affirm  indirectly  this  major ;  to  prove  it  is  to  estab- 
lish an  unexpressed  premise.  For  example : 

If  virtue  is  knowledge,  it  is  teachable. 

Do  you  admit  this  ?  Yes.  Then  that  is  merely  to  say  that  you  admit  "  All  forms 
of  knowledge  are  teachable."  Hence  this  hypothetical  conjunctive  affirms  a  men- 
tal judgment,  which,  taken  as  a  major,  would  necessitate  the  consequent. 


ANALYSIS    OF    CONDITIONALS.  239 

Let  us  now  follow  the  several  conjunctive  forms  (v,  §  2),  and,  re- 
garding them  as  ideal  enthymemes,  explicate  the  syllogisms  implied. 
It  should  be  observed  that  the  unexpressed  premise  in  each  case  con- 
sists of  terms  not  common  to  the  two  clauses. 

1  (a),  If  A  is  B,  A  is  C  ;  e.  g.,  If  man  is  responsible,  he  must  be  free. 

(B  is  C)  (The  responsible  must  be  free ;) 

If  A  is  B  (Barbara. )  If  man  is  responsible, 

then  A  is  C.  Then  man  must  be  free. 

1  (b),  If  A  is  not  B,  C  is  not  A ;  e.  g.,  If  bliss  has  no  anxieties,  ignorance  is  not  bliss. 

If  A  is  not  B  If  bliss  has  no  anxieties, 

and  (C  is  B)  (Cesare.)  (And  ignorance  has  anxieties,) 

then  C  is  not  A.  Then  ignorance  is  not  bliss. 

One  clause,  at  least,  mast  be  negative,  else  undistributed  middle. 

1  (c),  If  A  is  B,  B  is  C  ;  e.  g.,  If  rubies  are  clay,  some  clay  is  precious. 

(A  is  C)  (Rubies  are  precious  ;) 

If  A  is  B  (Darapli.)  If  rubies  are  clay, 

then  B  is  C.  Then  some  clay  is  precious. 

The  apodosis  must  be  particular;  else  illicit  minor. 

Variations  in  quantity  and  quality  in  the  above  will. yield  the  other 
moods  of  the  several  figures. 

1  (d),  If  A  is  B,  C  is  B  ;  e.  g.,  If  the  metals  are  fusible,  gold  is  fusible. 

If  A  is  B  'if  the  metals  are  fusible, 

and  (C  is  A)  (Barbara.)  (And  gold  is  a  metal,) 

then  C  is  B.  Then  gold  is  fusible. 

We  might  have  expected  this  to  yield  Fig.  4.  Bramantip,  but  its  di- 
rect resolution  into  the  first  figure  confirms  the  rejection  of  the  fourth. 
In  l(a)  the  minor  premise  is  given ;  in  l(d)  the  major. 

We  reach  now  the  second  form,  having  four  terms,  and  hence  no 
common  term.  For  the  sake  of  symmetry  we  rearrange  the  letters. 

2.  —  If  B  is  C,  A  is  D  ;  e.  g.,  If  the  wise  are  virtuous,  Socrates  was  innocent. 

(A  is  B)  (Socrates  was  AVISO  ;) 

If  B  is  C  (Sorites.)  If  the  Avise  arc  virtuous, 

and  (C  is  D)  (And  the  virtuous  are  innocent,) 

then  A  is  D.  Then  Socrates  was  innocent. 

It  is  evident  there  is  no  new  principle  involved  here.  The  proposi- 
tion is  an  ideal  enthymeme.  Supply  the  mental  premises,  and  it  falls 
at  once  into  an  established  form. 


240  OF    REASONIXGS. 

In  this  last  example  all  the  requisite  middle  terms  are  given. 
Clauses  may,  however,  be  logically  so  remote  from  each  other  that 
several,  perhaps  many,  intermediate  links  must  be  supplied  to  com- 
plete the  chain.  This  it  may  not  be  easy  to  do,  unless  the  unexpress- 
ed media  are  obvious.  It  is  the  part  of  the  speaker  or  writer  to  fur- 
nish these  to  us.  He  may,  at  the  outset,  as  preparatory,  lay  down  his 
chief  premise  hypothetically,  connecting  it  at  once  ideally  with  his 
ultimate  conclusion,  and  then  proceed  to  supply  the  media,  E.  g. : 

If  the  desire  for  distinction  is  an  essential  stimulus  to  industry, 

then  communism  is  antagonistic  to  the  progress  of  civilization. 

Here  arguments  might  be  needed  to  establish  the  antecedent,  and  per- 
haps a  long  series  to  show  that  it  necessitates  the  consequent.  So, 
also,  we  might  say,  "  If  the  tenth  proposition  of  Euclid  is  true,  then 
the  one  hundredth  is  true  also." 

As  an  actual  example  of  the  matter  before  us,  we  will  quote  a 
passage  from  Locke.9  He  is  speaking  contemptuously  of  the  Art 
of  Logic  and  of  the  syllogism,  saying,  "  God  has  not  been  so  spar- 
ing to  men  to  make  them  barely  two-legged  creatures,  and  left  it  to 
Aristotle  to  make  them  rational."  He  then  tries  to  show  that  logical 
forms  are  worse  than  useless,  being  confusing.  The  passage  is  curious 
as  an  effort  to  overthrow  that  which  it  uses,  and  therefore  unwittingly 
acknowledges.  He  says,  "  To  infer  is  nothing  but  by  virtue  of  one 
proposition  laid  down  as  true  to  "draw  in  another  as  true."  This  he 
illustrates  by  the  following  example :  "  If  men  shall  be  punished  in  an- 
other world,  then  men  can  determine  themselves."  lie  then  remarks, 
"  What  is  it  that  shows  the  force  of  this  inference,  and  consequently 
the  reasonableness  of  it,  but  a  view  of  the  connection  of  all  the  inter- 
mediate ideas  that  draw  in  the  conclusion  ? .  .  .  The  mind,  seeing  the 
connection  there  is  between  the  idea  of  men's  punishment  in  another 
world  and  the  idea  of  God's  punishing;  between  God's  punishing 
and  the  justice  of  the  punishment ;  between  justice  of  the  punishment 
and  guilt;  between  guilt  and  a  power  to  do  otherwise;  between  a 
power  to  do  otherwise  and  freedom ;  and  between  freedom  and  self- 
determination,  sees  the  connection  between  men  and  self-determina- 
tion. Now,  I  ask  whether  the  connection  of  the  extremes  be  not 
more  clearly  seen  in  this  simple  and  natural  disposition  than  in  the 
perplexed  repetitions  and  jumble  of  five  or  six  syllogisms?"  It  is 

*  Essay  on  tJw  Human  Understanding,  bk.  iv,  ch,  xvii,  "  Of  Keason," 


ANALYSIS    OF    CONDITIONALS.  241 

very  clear  that,  in  decrying  logical  form  and  showing  us  the  "  simple 
and  natural"  way,  he  has  developed  the  hypothetical  enthyrneme  into 
a  progressive  sorites,  stated  so  nearly  in  strict  logical  form  that  re- 
dressing is  needless. 

It  has  now  been  shown  that  all  the  reasoning  founded  on  or  im- 
plied in  the  contingent  hypothetical  is  thought  strictly  in  the  form  of 
the  Aristotelic  syllogism.  The  only  distinction  is  that  one  is  ideal, 
the  other  real.  We  now  add  that  viewed  as  a  conditional  proposition, 
apart  from  its  ideality,  it  differs  from  the  categorical  only  in  that  the 
latter  does  not  express  a  condition.  But,  in  fact,  every  logical  proposi- 
tion is  a  conclusion  conditioned  on  its  premises ;  so  all  reasoning  is 
conditional  reasoning.  The  conditional  character  may  not  appear  in 
expression,  but  it  belongs  to  all  thought.  It  adheres  to  every  possi- 
ble judgment  except  the  primitive  or  intuitive;  but  then  this  is  not 
thought.  A  judgment  truly  unconditional  neither  requires  nor  is  sus- 
ceptible of  proof;  it  cannot  appear  as  the  conclusion  of  a  syllogism. 
Or,  in  other  words,  every  syllogism  is  a  conditional  judgment  in 
which  the  premises  are  the  antecedents  and  the  conclusion  the  conse- 
quent. So,  then,  the  distinction  between  categorical  and  conditional, 
which  did  not  originate  with  Aristotle,10  is  a  mere  accident  of  expres- 
sion, ought  never  to  have  been  introduced,  and  ought  to  be  dismissed 
from  Logic.  The  distinction  between  categorical  and  hypothetical 
propositions  belongs  to  psychology,  is  of  no  logical  moment,  and 
ought  also  to  be  discarded.11 


10  See  Part  3d,  i,  §  7,  note. 

11  "  Of  the  truth  or  falsehood  of  propositions,  in  themselves,  Logic  knows  noth- 
ing, and  takes  no  account ;  all  in  Logic  may  be  held  true  that  is  not  conceived  as 
contradictor}'.     In  reasoning,  Logic  guarantees  neither  the  premises  nor  the  con- 
clusion, but  merely  the  consequence  of  the  latter  from  the  former ;  for  a  syllogism 
is  nothing  more  than  the  explicit  assertion  of  the  truth  of  one  proposition,  on  the 
hypotJicsis  of  other  propositions  being  true  in  which  that  one  is  implicitly  contained. 
A  conclusion  may  thus  be  true  in  reality  (as  an  assertion),  and  yet  logically  false 
(as  an  inference). 

In  a  certain  sense,  therefore,  all  logical  inference  is  hypothetical,  hypothetically 
necessary ;  and  the  hypothetical  necessity  of  Logic  stands  opposed  to  absolute  or 
simple  necessity.  The  more  recent  scholastic  philosophers  have  well  denominated 
these  two  species  the  necessitas  consequentice  and  the  necessitas  consequentis.  The 
former  is  an  ideal  or  formal  necessity ;  the  inevitable  dependence  of  one  thought 
upon  another,  by  reason  of  our  intelligent  nature.  The  latter  is  a  real  or  material 
necessity;  the  inevitable  dependence  of  one  thing  upon  another  because  of  its 
own  nature.  The  former  is  a  logical  necessity,  common  to  all  legitimate  come* 

16 


242  OF    REASONINGS. 

§  7.  The  hypothetical  forms  expressing  the  ideal  unreal  are  now 
to  be  considered.  These  are  always  in  the  past  tenses  of  the  sub- 
junctive mood.  In  usus  loguendi,  the  meaning  which  they  convey  is 
always  to  deny  the  reality  (hence  "  unreal ")  of  the  thought,  and, 
thus,  is  always  indirect.  There  seem  to  be  of  these  also  two  uses, — 
either  indirectly  to  declare  a  fact,  or  indirectly  to  declare  an  inference. 

We  exemplify  at  once  the  first  use : 

Were  he  king,  he  would  tyrannize. 

That  is  to  say,  he  is  not  king,  and  he  does  not  tyrannize. 
If  it  were  not  so,  I  would  not  say  it. 

That  is  to  say,  It  is  so,  and  I  do  say  it.  Thus  the  ideal  case  supposed 
is  denied  as  a  fact,  which  is  to  posit  its  opposite.  The  apodosis  makes 
its  statement  contrary  to,  or  in  spite  of,  the  real  fact,  which  is  thus  in- 
directly declared.13 

But  this  denial  of  the  supposition  is  not  the  ultimate  purport.  Yet 
more  indirectly,  these  propositions  convey  quite  another  meaning. 
They  seem  to  be  a  rhetorical  or  grammatical  or  linguistic  device  for 
saying  something  emphatically,  quite  aside  from  and  beyond  what 
the  words  directly  express,  and  which  it  would  perhaps  be  difficult 
to  state  directly.  For  example : 

Were  he  here,  I  would  tell  him. 

It  is  clearly  implied  that  he  is  not  here,  and  I  do  not  tell  him.  But 
to  state  these  patent  facts  is  not  the  object  of  my  saying  this.  The 
purport  seems  to  be  to  declare  my  state  of  mind,  perhaps  to  justify 
myself  in  reference  to  some  matter  in  question.  So,  briefly,  and  indi- 
rectly, but  quite  emphatically,  I  mean  to  affirm  that  I  am  so  disposed 
and  determined  in  this  case  that  no  circumstance  whatever  prevents 
my  action  now,  except  the  obvious  one  of  the  absence  of  the  object 
of  action';  my  mind  is  fully  made  up,  all  questions  settled,  and  there 
is  no  other  external  fact  I  know  of  to  hinder  me  from  thus  and  so ; 
now  you  know  what  I  think  and  feel  and  will  about  it.  Observe 

quence,  whatever  be  the  material  modality  of  its  objects.  The  latter  is  an  extra- 
logical  necessity,  over  and  above  the  syllogistic  inference,  and  wholly  dependent 
on  the  modality  of  the  matter  consequent.  This  ancient  distinction,  modern  philos- 
ophers have  not  only  overlooked  but  confounded." — Hamilton,  Discussions,  p.  146; 
12  The  past  tense  of  the  subjunctive  in  the  subordinate  clause  of  a  categorical 
proposition  has  the  same  force  of  denial.  E.  g.,  "I  would  I  were  a  boy"  implies 
that  I  am  not  a  boy. 


ANALYSIS    OF    CONDITIONALS.  240 

that  the  denial  implies  more  than  we  first  stated.  In  full  it  should 
be,  "  He  is  not  here,  and  therefore  only  I  do  not  tell  him."  This  is 
the  sole  condition,  the  only  reason  why  I  do  not  tell  him.  In  my 
present  disposition,  then,  there  is  none. 

Just  so  in  the  former  example,  "  If  he  were  king,  he  would  tyran- 
nize," the  meaning  is  "  He  is  not  king,  and  for  this  reason  only  he 
does  not  tyrannize,"  thus  declaring  indirectly  his  tyrannical  disposi- 
tion. Again,  "  If  it  were  not  so,  I  would  not  say  it,"  affirms  my  truth- 
fulness. In  the  following  example, 

"Were  this  beam  not  rotten,  it  would  serve, 

we  think  of  the  beam  as  rotten  and  unserviceable,  but  mean  primarily 
and  chiefly  to  affirm  the  suitableness  of  all  its  other  unnamed  quali- 
ties. In  the  trite  proverb 

If  wishes  were  horses,  beggars  would  ride, 

we  say  something  indirectly,  rhetorically,  about  beggars'  vain  longings, 
but  still  more  indirectly,  in  the  application  of  the  saw,  we  mean  to  re- 
buke extravagant  aspirations.  In  Macbeth's  speech, 

If  it  were  done  when  'tis  done,  then  'twere  well 
It  were  done  quickly, 

he  means  not  merely,  That  a  deed  outlives  itself,  must  give  us  pause ; 
but  rather  he  means  to  justify  his  hesitation.  Gay's  couplet, 

How  happy  could  I  be  with  either, 
Were  t'other  dear  charmer  away ! 

is  a  palimpsest  of  enamoured  distraction.  So  far  the  unreal  present. 
In  the  unreal  past,  we  have, 

If  thou  hadst  been  here,  my  brother  had  not  died, 

which  is  indirectly  a  strong  expression  of  confidence  in  superhuman 
power  and  love.  Might,  could,  or  should,  in  the  apodosis,  modifies 
the  meaning,  referring  the  matter  to  possibility,  ability,  or  duty. 

Propositions  of  this  sort  must  be  treated  logically  with  reference 
to  the  primary,  fundamental,  unexpressed  meaning,  and  not  to  the 
ostensible  ideal  statement,  nor  to  the  negation  of  fact,  which  are  sec- 
ondary, and,  taken  apart  from  the  primary  though  more  indirect  in- 
tent, are  generally  senseless.  They  are,  then,  to  be  viewed  and  inter- 
preted as  simple  categorical  judgments. 

Turning  now  to  the  unreal  proposition  declaring  an  inference,  we 
find  it  presents  a  further  peculiarity.  Let  us  recall  that  the  denial  of 


244  OF    REASONINGS. 

a  consequent  or  conclusion  denies  an  antecedent,  one  or  more  of  the 
premises  that  necessitate  it.  Then  let  us  consider  the  following : 

Whoever  talks  so  must  be  crazy ; 
Diogenes  talks  so ; 
.*.  Diogenes  must  be  crazy. 

Any  one  having  this  reasoning  in  mind  may  prefer,  for  emphasis  per- 
haps, to  state  it  indirectly.  By  expressing  ideally  a  denial  of  this 
mental  conclusion,  he  denies  ideally  the  fact  of  his  minor,  a  denial 
of  a  granted  fact,  and  hence  professedly  false,  and  thus  indirectly  he 
affirms  his  conclusion.  Thus  : 

Were  Diogenes  not  crazy,  he  would  not  talk  so ; 

meaning,  But  since  he  does  talk  so,  therefore  he  must  be  crazy.  So 
by  this  device,  this  custom  of  language,  we  mean  to  declare  the  op- 
posite of  our  words.  Our  reasoning  is  consciously  and  intentionally 
unreal,  and  goes  to  establish  its  opposite. 

For  further  illustration  we  renew  our  old  familiar  example, 
It  Plato  be  not  mortal,  he  is  not  a  man. 

Here  the  matter  is  stated  ideally  as  a  mere  contingency,  as  formally 
questionable.  But  in 

If  Plato  were  not  mortal,  he  would  not  be  a  man, 

the  matter  is  stated  as  absolutely  unreal,  thereby  declaring  emphati- 
cally, without  saying  so,  that 

Since  Plato  is  a  man,  he  must  be  mortal. 

But  in  the  following  affirmative  example  we  express  ourselves  more 
fully,  the  purposed  conclusion  being  distinctly  stated : 

No  rain  has  fallen  ;  for  if  there  had,  the  ground  would  be  wet. 

It  will  be  observed  that  this  is  essentially  the  reductio  ad  absurdum, 
as  is  sufficiently  manifest  in  the  following  examples : 

.  If  ignorance  were  bliss,  'twere  folly  to  be  wise. 
Were  all  the  prosperous  happy,  then  some  discontented 
would  be  happy.     (See  example  in  iv,  §  3.) 

These  conclusions  are  evidently  self-contradictory  and  absurd.  Hence 
the  contradictory  of  their  antecedents  is  true.  Again : 

Were  Christianity  not  from  God, 

it  would  not  have  been  accompanied  by  credible  miracles; 
Were  its  miracles  unworthy  of  credit, 

they  would  not  have  been  attested  in  the  manner 

in  which  it  has  been  proved  they  were.    (See  the  argument  in  iv,  §  4.) 


ANALYSIS    OF    CONDITIONALS.  245 

The  formal  reductio  ad  absurdum,  appropriately  called  the  method  of 
indirect  demonstration,  is  conveniently,  elegantly,  and  usually  stated 
in  these  ideal  unreal  forms.  For  an  instance  refer  to  iv,  §  8,  ex.  51. 

We  conclude  that  the  ideal  unreal  form  of  the  hypothetical  propo- 
sition, when  declaring  an  inference  or  offered  as  proof,  reasons  indi- 
rectly. By  an  ideal  denial  of  an  unexpressed  conclusion,  it  denies  an 
unexpressed  but  unquestionable  premise,  which  denial,  being  absurd, 
impliedly  affirms  the  truth  and  reality  of  that  conclusion.13 

§  8.  It  is  needful  now  to  revert  to  the  form  commonly  known  in 
Logic  as  the  hypothetical  conjunctive  syllogism  (v,  §  5).  Aristotle  ig- 
nores all  forms  of  the  so-called  conditional  syllogism.  In  one  place  in 
his  Analytics,  however,  he  describes  the  process  now  known  as  the 
hypothetical  syllogism,  but  denies  that  it  is  a  syllogism.14  lie  was  right. 
Conditional  syllogisms  were  nevertheless  introduced  into  Logic  by  his 
immediate  successor  in  the  Lyceum,  Theophrastus,  were  accepted  by  his 
rival  Eudemus,  and  were  adopted  by  the  Stoics.  They  have  received  the 
sanction,  in  one  way  or  another,  of  nearly  all  logicians  down  to  the  pres- 
ent time.  Especially  were  they  endorsed  and  developed  by  Boethius, 
and  his  great  authority  has  given  them  a  permanent  place  in  Logic. 
Still  there  has  been  a  continual  wrangle  about  the  details  of  the  sys- 
tem, betraying  a  deep  dissatisfaction,  although  their  right  to  be  con- 
sidered special  modes  of  reasoning  has  hardly  been  questioned.  The 
admiring  commentators  of  Aristotle  have  generally  felt  it  needful  to 
apologize  for  the  hiatus  which  his  disregard  of  them  makes  in  his  Ana- 
lytics ;  excepting,  however,  Saint-Hilaire,  who,  in  his  translation  of  the 

13 1  have  nowhere  seen  a  development  of  the  matter  contained  in  this  and  the 
previous  sections,  nor,  indeed,  of  the  views  presented  throughout  this  general  discus- 
sion. Hardly  a  hint  is  to  be  found  in  our  Logics.  Arnauld  in  a  single  sentence 
speaks  of  the  enthymemic  character  of  conditionals.  Mansel  (App.  to  Aldrich,  p.  240) 
writes  two  sentences  in  which  the  doctrine  glimmers.  The  most  explicit  state- 
ment I  have  encountered  is  from  Titius  (Ars  Cogitandi,  ch.  xii),  as  follows :  "  Con- 
ditionalis  seu  hypotheticus  nihil  aliud  est  quam  enthymema  vel  sine  majore  vel 
minore."  "Syllogismus  disjunctivus  est  enthymema  sine  majore."  "Sequitur 
nullum  peculiare  concludendi  fundamentum  vel  formam  circa  syllogismos  condi- 
tionales  occurrere,  nam  argumentationes  irnperfectas,  adeoqqe  materiam  syllo- 
gismorum  regularium  illi  continent."  My  own  views  were  worked  out  before  this 
caught  my  ey-e,  but  it  seems  they  are  not  altogether  new. 

14  Anal.  Prior,  i,  32,  7.  "  If  because  man  exists,  it  is  necessary  that  animal 
should  be ;  and  animal  existing,  that  there  should  be  essence ;  then,  because  man 
exists,  essence  must  necessarily  be.  But  this  is  not  yet  syllogistically  inferred,  for 
the  propositions  do  not  subsist  as  we  have  said  they  should," 


240  OF    REASONINGS. 

Organon,  insists  that  they  are  therein  recognized.15  Emboldened  by 
this  generally  admitted  silence  of  Aristotle,  let  us  question  their  title, 
and  judge  whether  the  Stagyrite  did  his  work  only  by  half. 

A  number  of  modern  writers  on  Logic,  recognizing  hypothetical 
syllogisms  as  distinct  modes  of  reasoning,  endeavor  in  various  ways  to 
show  that  they  may  be  reduced  to  Aristotelic  forms.  But  are  they 
reasonings  at  all?  We  recall  that  deductive  inference  is  of  two  kinds, 
mediate  and  immediate.  In  mediate  inference  we  determine  the  rela- 
tion of  two  notions  through  a  third,  the  middle  or  medium.  A  syllo- 
gism is  the  formal  expression  of  this  mediate  process,  and  hence  a 
middle  term  is  its  essential  feature.  Now  hypothetical  syllogisms,  so 
called,  contain  no  middle  term.  Therefore  they  are  not  syllogisms, 
not  expressive  of  reasoning  at  all.  Inspect  the  following : 

If  law  prevails,  our  rights  are  secure  ;— Major  Premise. 

MODUS  PONENS.     Cut  law  does  prevail ; =  Minor  Premise. 

.*.  Our  rights  are  secure =  Conclusion. 

There  is  no  term  here  with  which  the  two  terms  found  in  the  conclu- 
sion are  compared  in  the  premises.  There  are  in  all  four  terms,  and 
all  found  in  the  so-called  major  premise.  The  so-called  minor  intro- 
duces no  new  matter,  and  has  nothing  in  common  with  the  conclu- 
sion, as  necessarily  occurs  in  the  true  syllogism. 

16  "  Aristote  n'a  pas  omis  davantage  les  syllogismes  hypothetiques,  dont  on  a 
voulu  faire  honneur  encore  a  ses  eleves  Theophraste  et  Euderne.  Les  syllogismes 
hypothetiques  sont  ce  qu'  Aristote  appelle  les  syllogismes  d'hypothese,  de  con- 
vention. II  en  avait  traite  tout  au  long  dans  un  ouvrage  que  le  temps  nous  a  ravi, 
mais  que  lui-meme  mentionne  dans  le  Premiers  Analytiques,  i,  44,  4." — Logiquc 
d' Aristote,  Preface,  p.  Ix.  St.-Hilaire  then  proceeds  to  a  discussion.  See,  also, 
tome  iv,  top.  i,  8,  9.  He  has  against  him,  however,  Waltz  (see  Comment,  on  Anal. 
Prior,  i,  44)  and  Hamilton  (see  Discussiojis,  p.  151).  For  references  to  other  au- 
thorities, see  Hamilton's  Logic,  p.  613, note;  and  Grote's  Aristotle,  p.  243, note. 

In  the  passage  above  referred  to  by  St.-Hilaire,  Aristotle  promises  to  treat  at 
some  future  time  of  Syllogisms  from  Hypothesis,  but  more  probably  the  treatise 
was  never  realized,  as  there  are  no  extant  references  to  it.  Against  St.-Hilaire  it 
can  be  proved  that  by  Syllogisms  from  Hypothesis  Aristotle  meant  the  various 
forms  of  the  Rcductio  ad  impossibile,  and  not  at  all  what  are  now  known  as  Hypo- 
thetical Syllogisms.  Moreover,  the  historical  fact  already  stated,  that  Theophrastus 
changed  the  Aristotelic  sense  of  the  term  " categorical,"  which  was  simply  "af- 
firmative," to  the  sense  opposed  to  "hypothetical,"  is  evidence  that  he,  and  not  his 
master,  was  the  inventor  of  the  hypothetical  system.  I  have  not  seen  the  point 
mentioned,  but  the  change  seems  clearly  to  indicate  that  Aristotle  had  no  such  op- 
posed term,  and  that  Theophrastus  found  a  special  need  for  one  to  mark  a  new 
distinction. 


ANALYSIS    OF    CONDITIONALS.  247 

Impressed  by  the  absence  of  a  middle  term,  Kant  declared  these 
pseudo-syllogisms  to  be  forms  of  immediate  inference.  Now,  im- 
mediate inference  is  merely  from  a  given  judgment  to  infer  directly, 
i.  e.,  without  a  medium,  a  different  judgment.  Let  us  inspect  the 
above  example  presented  in  a  slightly  different  form  : 

If  Law  prevails,  then  our  rights  are  secure. 
Law  prevails,  then  our  rights  are  secure. 

Now  here  is  an  absolute  iteration  of  thought,  stated  first  as  suppositi- 
tious, then  as  assertorial.  The  subject  is  the  same.  The  predication 
is  the  same.  The  second  judgment,  then,  is  not  different  logically 
from  the  first,  and  therefore  this  cannot  be  an  immediate  inference.18 
Another  example,  to  vary  the  forms : 

If  my  debtors  are  honest,  they  will  repay  me ; 

(1)  My  debtors  are  honest,  they  will  repay  me; 

(2)  Some  are  honest,  some  will  repay  me ; 

(3)  Tbis  one  is  honest,    he   will  repay  me. 

In  2  and  3  there  is  a  diminution  of  quantity.  Is  not  either  of  these 
an  immediate  inference  from  the  major  premise  by  subalternation? 
No ;  for  subalternation  concludes  that  "  some  are,"  because  "  all  are ;" 
which  is  not  here  the  case,  since  we  may  be  able  to  affirm  2  or  3, 
when  1  (all)  is  not  true." 

If,  then,  these  forms  are  not  inferences  of  either  kind,  what  are 
they  ?  Three  views  are  possible.  First,  they  are  forms  of  speech 
indicating  a  transfer  from  the  ideal  to  the  real  mode  of  thought.  It 
has  been  already  observed  that  we  cannot  pass  from  the  ideal  to  the 
real  without  some  ground.  We  may  say,  ideally,  If  law  prevails,  a  cer- 
tain consequence  follows ;  but  whether  law  does  really  prevail,  or  not, 
is  not  determined  by  anything  in  that  proposition.  We  must  seek 
ground  for  the  affirmation  elsewhere ;  and  when  discovered,  then,  but 
not  until  then,  can  we  pass  to  the  real,  and  assort — Law  prevails. 
Now,  by  virtue  of  this  discovered  ground  we  can  declare  the  conclu- 
sion, already  stated  ideally,  to  be  real  also — Our  rights  are  secure. 
The  discovered  ground  may  not  be  sufficient  to  establish  the  reality 

16  Let  us  be  reminded  that  progress  from  doubt  to  certainty  is  a  change  in  con- 
viction, in  degree  of  belief,  in  feeling,  but  is  not  a  change  in  thought. 

17  In  the  treatment  of  these  forms  Hamilton  wavers.     In  his  Lectures  he  ac- 
cepts the  old  doctrine.     In  his  latest  note  (Logic,  p.  603)  he  almost  reaches  the 
point  of  rejecting  them,  saying,  "If  inferences  at  all,  they  are  immediate,  and  not 
mediate."    See  also  his  note  in  Discussions,  p.  151. 


248  OF    REASONINGS. 

of  more  than  a  part ;  if  so,  we  can  conclude  the  reality  of  a  part  only 
— Some  of  my  debtors  will  repay  me.  Here  it  appears  that  the 
hypothetical  conjunctive  proposition  is  the  ideal  entbymeme;  that 
the  so-called  conjunctive  syllogism  is  not  a  syllogism  at  all,  nor  ex- 
pressive of  reasoning  or  inference  of  any  kind ;  that  it  merely  reiter- 
ates the  enthymeme  as  real ;  that  it  indicates  a  transfer  from  the  ideal 
to  the  real  on  unexpressed  grounds ;  that  it  is  simply  a  formal  mode 
of  announcing  the  ideal  premise  established  as  real,  in  whole  or  in 
part,  and  the  consequent  reality  of  the  conclusion.  The  reasoning 
implied  is  purely  Aristotelic,  and  is  duplicated  in  the  two  enthymemes. 
A  second  view  considers  the  conjunctive  proposition  as  merely  an 
affirmation  of  sequence,  its  second  prepositional  use.  In  this  view 
the  so-called  syllogism  consists  of  three  propositions.  The  conjunc- 
tive affirms  the  necessary  coexistence  of  the  other  two  judgments,  or, 
better,  it  affirms  only  a  consequence  from  one  to  the  other.  One  of 
these  affirms  categorically  the  existence,  in  whole  or  in  part,  of  one 
fact.  The  other  infers  the  existence  of  another  fact. 
x  is ;  but  if  x  is,  y  is ;  then  y  is. 

Here  again  is  an  enthymeme.  In  this  view,  however,  the  enthymeme 
lies  solely  in  the  two  categorical  judgments,  but  is  strengthened  by  a 
distinct  affirmation  of  their  necessary  sequence.  The  reasoning,  then, 
lies  not  at  all  in  any  inference  from  the  hypothesis  to  the  assertion, 
but  wholly  in  the  relation  of  the  two  categorical  judgments  as  pre- 
mise and  conclusion.  This  reasoning  is  purely  Aristotelic. 

A  third  view  is  that  the  conjunctive  proposition  affirms  indirectly 
an  unexpressed  major  premise.18  In  this  view  the  so-called  hypo- 
thetical syllogism  affirms  the  three  real  propositions  of  a  categorical 
or  Aristotelic  syllogism.  It  is  not  now  an  enthymeme,  unless  the  in- 
directness of  the  major  be  held  to  bestow  this  character,  and  not  the 
slightest  ground  appears  on  which  to  distinguish  it  as  a  special  form 
or  mode  of  reasoning. 

It  follows  that  the  axiom  of  Sufficient  Reason10  is  an  entire  super- 
fluity in  Logic.  The  three  Primary  Laws,  and  the  rules  evolved  from 
them, -are  all-sufficient;  for  every  case  of  a  violation  of  the  axioms  of 
Reason  and  Consequent  will  be  found,  on  developing  the  enthymeme, 
to  be  a  violation  of  one  or  another  of  the  general  rules  of  the  Aris- 
totelic syllogism.  Hamilton  latterly  suspected  that  the  Platonico- 
Leibnitzian  Law  was  out  of  place  in  Logic,  and  Mansel  definitely 

18  See  supra  foot-note  8.  "  Sec  Part  1st,  ii,  §  7. 


ANALYSIS    OF    CONDITIONALS.  249 

reached  this  conclusion.  There  can  be  no  doubt  that  it  should  be 
relegated  to  the  realm  of  Metaphysics,  whence  it  was  drawn.20 

§  9.  It  remains  to  indicate  more  explicitly  that  disjunctive  and 
other  compound  conditional  propositions  are  merely  enthymemes. 
We  here  speak  of  disjunctives  as  compounds,  and  it  is  easy  to  show 
that  they  are  so.  Every  disjunctive  having-  two  subcontrary  members 
consists  of  two  hypotheticals,  which  may  be  explicated  thus : 

C  is  either  D  or  E ;  c.  g.,  God  is  either  loved  or  feared ; 
yields  If  C  is  not  D,  C  is  E ;  e.  g.,  If  God  is  not  loved,  he  is  feared  ; 
and  If  C  is  not  E,  C  is  D ;  e.  g.,  If  God  is  not  feared,  he  is  loved. 

When  the  opposition  is  contradictory,  as  in  "God  is  cither  trust- 
worthy or  untrue,"  the  analysis  yields  four  hypotheticals,  the  two 
others  being : 

If  C  is  D,  C  is  not  E  ;  e.  g.,  If  God  is  trustworthy,  he  is  not  untrue  ; 
If  C  is  E,  C  is  not  D ;  e.  g.,  If  God  is  untrue,  he  is  not  trustvvorth}'. 

Now,  the  disjunctive  proposition  being  merely  a  double  or  quadruple 
hypothetical,  it  follows  that  what  has  been  proved  of  hypotheticals 
is  true  of  it.  Moreover,  it  is  easy  to  show  that  the  so-called  disjunc- 
tive syllogism  is  merely  a  reiteration  of  the  enthyrneme  expressed  by 
one  or  another  of  these  constituent  hypotheticals.  Thus : 

C  is  either  D  or  E  explicates  into 

(What  is  not  D  is  E ;)  (What  is  not  E  is  D  ;) 

If  C  is  not  D  ;  —and—  If  C  is  not  E ; 

then  C  is  E.  then  C  is  D. 

These  two  simple  syllogisms  in  Barbara  or  Darii  correspond  to  the 
Modus  T.ollendo  Ponens.  In  case  of  contradictories,  we  have  also : 

(What  is  D  is  not  E ;)  (What  is  E  is  not  D  ;) 

If  C  is  D ;  —and—  If  C  is  E ; 

then  C  is  not  E.  then  C  is  not  D. 

These  two  latter  syllogisms  in  Celarent  or  Ferio  correspond  to  the 
Modus  Ponendo  Tollens.  It  appears,  then,  that  the  disjunctive  prop- 
osition condenses  or  involves  in  one  compound  statement  two  or  four 
hypothetical  enthymemes ;  and  that  the  pretended  disjunctive  syllo- 
gism is  merely  a  restatement  or  explication  of  some  one  of  these  en- 
thymemes either  as  ideal  or  as  real. 

20  See  Hamilton's  Logic,  p.  62,  and  note ;  also  p.  251.  See  also  Hansel's  Aldrich, 
note  p.  235  ;  and  Prolegomena  Logica,  p.  193. 


250  OF    REASONINGS. 

The  conjunctive-disjunctive  proposition  is  an  acknowledged  com- 
pound, and  the  dilemma  is  obviously  made  up  of  conjunctives  and 
disjunctives.  It  is  needless  to  trace  the  principle  through  these  intri- 
cate forms.  It  may  be  well,  however,  to  observe  that  the  former  is 
merely  a  disparate  disjunctive  proposition,  one  member  of  which  has 
been  reduced  to  the  conjunctive  form.  E.  g. : 

Man  must  bo  either  capable  of  progress,  or  a  brute,  or  a  divinity. 

If  man  is  incapable  of  progress,  he  must  be  either  a  brute  or  a  divinity. 

§  10.  Ought  not,  then,  these  conditional  forms,  these  pseudo-syllo- 
gisms, to  be  banished  from  Logic  ?  By  no  means ;  for  they  are  true, 
natural,  and  very  common  modes  of  expressing  thought,  and  hence 
call  for  logical  analysis  and  treatment.  Nothing  is  more  common 
than  for  a  reasoner  at  the  outset  to  state  hypothetically  his  premise 
and  conclusion.  This  he  does  for  the  sake  of  clearness,  and  to  sho\v 
whither  he  is  tending.  E.  g. : 

If  the  prisoner  was  sane,  then  he  is  responsible  for  his  act. 

His  first  argument  may  be  to  show  the  necessity  of  the  sequence 
herein  declared.  As  accusing  counsel,  he  next  endeavors  to  establish 
this  antecedent  minor,  perhaps  by  showing  the  deliberation  of  the 
agent,  his  consistency,  his  motives,  etc.,  etc. ;  and,  it  may  be,  he  brings 
in  medical  evidence.  "When  the  argument  is  complete,  he  closes  by 
declaring  categorically : 

The  prisoner  was  sane,  therefore  he  is  responsible  for  his  act. 

Hence  Hamilton,  in  one  place,  proposes  to  call  the  various  conditional 
forms  "  preparations  for  argumentation." 

Again,  many  of  these  conditional  forms  present  exceedingly  con- 
densed expressions  of  reasonings  through  which  the  mind  darts  with 
rapidity,  and  unless  the  thinker  is  familiar  with  their  analysis,  he  is 
in  danger,  especially  in  the  more  intricate  dilemmatic  forms,  of  paral- 
ogism, or  of  being  imposed  upon  by  sophism.  Hence  these  were 
favorite  forms  with  the  Greek  Sophists,  and  indeed  are  still  preferred 
by  all  who  wish  to  make  the  worse  appear  the  better  reason.  On  the 
other  hand,  their  condensation  gives  to  a  just  argument  weight,  and 
logical  and  rhetorical  force.  They  should,  then,  be  discussed,  not  only 
as  subjects  of  analysis,  but  also  because  of  the  practical  advantage  re- 
sulting from  their  close  examination. 

It  is  clear,  however,  that  their  nomenclature  ought  to  be  changed. 
The  unfortunate  misapplication  of  the  terms  "  syllogism,"  "  major  and 


ANALYSIS    OF    CONDITIONALS.  251 

minor  premise,"  "  mood,"  etc.,  etc.,  and  the  attempt  to  enunciate  rules 
and  methods  of  reduction  parallel  to,  but  distinct  from,  those  of  the 
true  syllogism,  has  filled  Logic  for  centuries  with  confusion  and  error. 
But  so  deeply  rooted  in  logical  literature,  and  so  widely  spread  is  this 
false  system  and  terminology,  that  the  needed  correction  can  be  made 
only  by  the  highest  authority. 

It  is  a  great  satisfaction,  however,  to  say  that  the  omission  by  Aris- 
totle of  any  treatment  of  conditionals,  so  far  from  calling  for  apology, 
may  be  adduced  as  an  evidence  of  the  profound  and  thorough  charac- 
ter of  his  Analytics.  Logicians  should  respect  the  silence  of  the 
master,  and  when  its  significance  is  not  clear,  it  would  be  well  and 
modest  to  imitate  it. 

To  sum  up :  There  are  but  two  kinds  of  deductive  inference,  the 
immediate  and  the  mediate.  The  analysis  of  Aristotle  is  limited  to 
these  kinds.  The  various  forms  of  conditional  propositions  are  essen- 
tially hypothetical  conjunctives,  or  ideal  enthyrnemes.  There  is  no 
such  thing  as  conditional  reasoning  distinct  from  categorical ;  but  all 
conditional  is  categorical,  and  all  categorical  is  conditional.  The  so- 
called  conditional  syllogisms  are  not  syllogisms  at  all,  nor  inferences 
of  any  kind ;  but  are  mere  reiterations  of  the  enthymeme  as  real. 
They  do  not,  therefore,  require  a  distinct  system  of  rules  and  forms, 
but  rightly  take  their  places  under  the  Aristotelic  system,  which  is 
an  exhaustive  analysis  of  deductive  thought. 


PAET  FIFTH.— OF  FALLACIES. 


I.  DISTRIBUTION. 

§  1.  The  Primary  Laws  of  Thought,  whose  consequences  have  been 
expounded  in  the  foregoing  pages,  are  derived  from,  or  formulated  in 
accordance  with,  the  ultimate  original  constitution  of  mind.  The}7 
are  necessary ;  that  is,  their  contradictories  are  inconceivable,  they 
cannot  be  doubted  or  questioned  by  the  human  mind.  It  follows  that 
mental  processes  and  results  in  strict  conformity  with  them  are  equal- 
ly necessary  in  the  same  sense.  But  these  Laws  arc  not  necessary  in 
the  sense  that  they  must  perforce  be  obeyed.  Mental  processes  do 
not  necessarily  conform  to  them.  They  declare  how  we  must  think, 
if  we  think  consecutively  ;  but  they  are  not  inviolable.  Our  thoughts 
are  not  determined  in  their  course,  like  the  planets,  by  inexorable 
forces.  The  planet  has  no  choice.  Laws  of  thought  arc  impressed 
upon  our  mental  constitution  just  as  laws  of  health  are  impressed 
upon  our  physical  constitution.  The  latter  we  may  consciously  or  un- 
consciously disregard,  but  the  inevitable  consequence  is  disease ;  the 
former  we  may  likewise  disregard,  but  only  to  incur  the  deadlier  con- 
sequence of  error  and  folly. 

A  System  of  Logic,  a  Theory  of  Thought,  is  complete  on  its  posi- 
tive side,  in  showing  how  we  do  and  must  think,  if  we  think  correct- 
ly and  fruitfully.  But  this  cannot  be,  without  contemplating  at  the 
same  time  the  possibility  of  error,  and  modes  of  incorrect  thinking. 
The  Law  of  Relativity  declare^  that  every  notion  has  its  opposite, 
that  the  notion  of  truth  implies  the  notion  of  error,  that  the  notion 
of  correct,  regulated  thought  implies  the  notion  of  incorrect,  unregu- 
lated thought.  If  all  objects  were  white,  and  of  the  same  shade, 
none  would  be  distinguishable.  Hence  the  scholastic  maxim  :  Contra- 
riorum  eadem  est  scientist.  We  cannot  consider  the  observance  of  a 
law  apart  from  its  violations ;  the  one  implicates  the  other.  When 
good  reasoning  is  exhibited,  bad  reasoning  must  be  conceived  as  at 
least  possible,  else  the  good  cannot  be  conceived  as  good.  "  According 


DISTRIBUTION.  250 

to  old  definitions,"  says  De  Morgan,  "  bad  reasoning  is  a  reasoning, 
syllogismus  sophlsticus  is  one  kind  of  syllogism,  and  in  a  certain  old 
book  the  fruits  of  demonstration  are,  science,  opinion,  and  ignorance, 
the  latter  derived  from  bad  demonstration,  what  we  would  now  call  no 
demonstration."  Hence,  all  along  through  the  present  treatise,  it  has 
been  necessary,  in  showing  the  methods  of  correct  reasoning,  to  glance 
at  the  incorrect.  Examples  violating  the  rules  have  frequently  been 
given.  But  as  our  view  has  been  steadily  fixed  on  the  positive  side 
of  the  theory,  the  negative  side,  or  incorrect  thinking,  has  been  very 
imperfectly  developed.  To  the  satisfactory  completion  of  our  task 
it  is  needful  now  that  we  take  a  comprehensive  and  systematic  view 
of  the  violations  of  the  Laws  of  Thought. 

If  any  further  justification  were  needed  for  adding  to  our  treatise 
a  discussion  of  Fallacies,  it  might  be  found  in  the  valuable  practical 
results  following  the  study  of  them.  It  contributes  greatly  to  a  habit 
of  clear  and  logically  consecutive  thought,  that  one  be  familiar  with 
the  various  dangers  that  threaten  it,  with  the  slips  to  which  it  is  in- 
clined, with  the  snares  which  environ  it.  Error,  seen  to  be  error,  is 
harmless ;  it  is  only  when  in  the  guise  of  truth  that  it  is  dangerous. 
But  error,  thus  disguised,  abounds,  and  a  practical  skill  in  detecting 
and  exposing  it  is  of  inestimable  value.  So  important  is  this  con- 
sidered, that,  while  Logic  might  justly  confine  itself  to  very  simple 
illustrations  of  the  violations  of  its  rules,  it  is  customary  to  extend 
the  examination  to  quite  intricate  and  difficult  cases,  and  to  consider 
many  varieties  of  error. 

Moreover,  if  it  can  be  shown,  as  we  progress,  that  all  kinds  of  falla- 
cious thinking  are  at  bottom  violations  of  established  logical  rules,  it 
will  go  far  to  confirm  the  doctrine  of  this  treatise,  that  the  Aristotelic 
syllogism  is  the  unit  of  all  mediate  thought. 

§  2.  Bacon  was  the  first  philosopher  who  attempted  a  systematic 
enumeration  of  the  various  sources  of  human  error.1  He  made  of 
them  a  quaint  classification  into  four  genera,  under  the  significant 
name  of  "Idols"  (a^oc,  'an  image),  in  the  sense  of  illusions,  described 
as  if  presented  in  a  magic  mirror.  He  says :  "  I  do  find,  therefore, 
in  this  enchanted  glass  four  idols,  or  false  appearances,  of  several  dis- 
tinct sorts,  every  sort  comprehending  many  subdivisions."  These  he 
enumerates  as  follows : 

1  Novum  Organum,  lib.  i ;  Summary  of  Part  ii ;  Aphorism  38  sq. 


254  OP    FALLACIES. 

Idola  tribus ;  Idols  of  the  nation  or  tribe,  to  which,  from  certain 
common  weaknesses  of  human  nature,  we  are  universally  liable. 

Idola  specus  ;  Idols  of  the  den  or  cave,  which,  from  the  peculiar 
(I.  positions  and  circumstances  of  individuals,  mislead  them  in  differ- 
ent manners. 

Idola  fori ;  Idols  of  the  forum,  public  assembly,  or  bar,  arising 
from  the  current  usage  of  words  which  represent  things  much  other- 
wise than  as  they  really  are. 

Idola  theatri  ;  Idols  of  the  theatre,  which  false  systems  of  philos- 
ophy and  erroneous  methods  of  reasoning  have  introduced.2 

The  intellect,  therefore,  may  be  perverted  by  mixing  with  pure  rea- 
son our  gregarious  affections,  or  our  individual  propensities ;  the  false 
suggestions  involved  in  language,  or  the  imposing  delusions  of  re- 
ceived theories.  Bacon  declares  that  the  doctrine  concerning  these 
Idols  bears  the  same  relation  to  the  interpretation  of  nature  as  the 
doctrine  concerning  sophistical  paralogisms  bears  to  deductive  Logic. 
Whcwell,  however,  thinks  that  his  precepts  concerning  these  Idols 
"have  little  to  do  with  Natural  Philosophy."3  And  moreover  the 
class  Idola  fori,  the  snares  of  language,  corresponds  pretty  nearly  with 
Aristotle's  Fallacies  in  dictione. 

§  3.  The  next  most  notable  attempt  at  a  classification  of  error  is 
that  of  Mill.*  lie  uses  the  word  "fallacies"  to  include  all  kinds  of 
intellectual  error,  and  discovers  five  genera : 

1.  Fallacies  a  priori; — Errors  in  simple  inspection,  arising  from 
natural  prejudices. 

2.  Fallacies  of  Observation ; — Errors  in  the  ground  of  induction, 
arising  from  either  mal-observation  or  non-observation  of  the  facts. 

3.  Fallacies  of  Generalization ; — Errors  in  the  process  of  induction, 
arising  from  a  misconception  of  the  legitimate  mode  of  drawing  con- 
clusions from  observed  facts. 

4.  Fallacies  of  Ratiocination ; — Errors  in  argumentation,  provided 
against  in  the  rules  of  the  Syllogism. 

5.  Fallacies  of  Confusion ; — Errors  arising  from  evidence  being  con- 
ceived in  so  indistinct  a  manner  as  not  to  produce  any  clear  conscious- 
ness of  the  means  by  which  the  conclusion  is  reached. 

*  See  Hallam's  Literature  of  Europe,  Part  iii,  ch.  iii,  §§  58,  59.  Read,  also,  the 
admirable  chapter  xx,  Part  3d,  of  the  Port-Royal  Logic,  on  "Sophisms  common  in 
Civil  Life." 

3  Philosophy  of  Discovery,  ch,  xv,  §  20.  4  Logic,  bk.  v,  ch.  ii. 


DISTRIBUTION.  255 

Nos.  2  and  8  are  Inductive  Fallacies ;  No.  4,  Deductive ;  No.  5,  a  kind 
of  omnium  gatherum  of  sorts  and  cases  that  do  not  come  under  one  of 
the  other  heads.  It  occupies  the  whole  ground  included  by  Aristotle's 
fallacies  in  dictione,  and  extra  dictionem.  It  will  appear,  however, 
in  the  sequel,  that  these  also  are  Deductive  Fallacies,  violating  syllo- 
gistic rules. 

§  4.  The  arrangement  adopted  in  most  English  manuals  of  Logic  is 
that  of  Whately.6  He  rejects  Aristotle's  division  as  indistinct,  and 
divides  Fallacies  into  Logical  or  Formal,  and  Non-Logical  or  Material. 
The  first  class  includes  all  cases  "  where  the  conclusion  does  not  fol- 
low from  the  premises ;"  these  violate  the  syllogistic  rules.  As  Non- 
Logical,  or  Material,  he  reckons  all  cases  "  where  the  conclusion  does 
follow  from  the  premises ;"  but  where  cither  the  premises  are  unduly 
assumed,  or  the  conclusion  is  irrelevant  to  the  point  in  dispute.  Surely 
this  passes  beyond  the  sphere  of  Logic.  It  might,  perhaps,  be  justi- 
fied by  an  appeal  to  Aristotle,  who  in  one  place  defines  a  fallacy  as 
"  a  reasoning  which,  either  in  matter  or  form  or  both,  appears  to  be 
that  which  it  is  not.6  In  apparent  accord  with  this,  to  which,  how- 
ever, he  makes  no  reference,  Whately  goes  on  to  insert  an  intermediate 
class,  the  Semi-Logical  Fallacies,  which  are  described  as  those  whereof 
"  the  fault  lies  partly  in  the  form,  and  partly  in  the  matter."  I  do 
not  understand  this.  It  would  seem  rather  to  be  a  double  fault.  Any 
error  in  form  is  of  itself  total  and  fatal.  As  for  Non-Logical  Falla- 
cies, they  are  ex  vi  termini  out  of  the  pale.  Hamilton,  however,  has 
adopted  this  distribution.7 

With  the  matter  of  an  argument,  as  to  the  truth  or  falsity  of  its 
premises,  unless  they  be  self-contradictory,  Logic  has  nothing  to  do, 
but  only  with  the  validity  of  the  conclusion  from  given  premises. 
All  that  relates  to  the  collection  of  true  premises  with  respect  to  the 
vegetable  world  belongs  to  Botany;  with  respect  to  the  heavenly 
bodies,  to  Astronomy ;  with  respect  to  the  relation  of  man  to  his 
creator,  to  Theology.  Were  it  within  the  province  of  Logic,  it  would 
require  the  extent  of  an  encyclopaedia  to  enter  upon  questions  con- 
nected with  the  matter  of  syllogisms.  Thus  Aristotle :  "  All  the 
sources  of  fallacy  could  not  be  enumerated  if  we  consider  the  truth  of 
the  premises.  This  would  require  omniscience,  for  the  sources  are  pos- 
sibly infinite,  and  every  science  has  false  principles  peculiar  to  it.  Our 

6  Logic,  bk.  iii,  §§  1-4.  fl  Topica,  i,  1,  3.  T  See  Logic,  Lect.  xxiii. 


250  OF    FALLACIES. 

present  task,  then,  is  to  trace  the  fallacies  common  to  every  science. 
This  we  may  do,  for  they  are  limited  in  number.  The  logician  must 
investigate  the  common  fallacies  that  belong  to  no  particular  sphere." 8 
We  shall  accordingly  limit  our  attention  to  formal  fallacies ;  material 
fallacies  are  excluded.  We  shall  consider  matter  only  in  so  far  as  it 
may  be  needful  to  inspect  it  in  order  to  discover  a  fault  of  form.  But 
then,  indeed,  we  shall  undertake  to  show  that  nearly  all  the  kinds  of 
fallacies  usually  classed  as  material  are  at  bottom  formal,  violating 
syllogistic  rules,  and  we  shall  adopt  the  old  Aristotelic  and  scholastic 
classification  as  sufficient  to  this  end.  All  logical  fallacies,  properly 
speaking,  are  formal  fallacies. 

§  5.  A  Fallacy  is  commonly  described  as  "any  unsound  mode  of 
arguing,  which  appears  to  demand  our  conviction,  and  to  be  decisive 
of  the  question  in  hand,  when  in  fairness  it  is  not."  Says  Kant :  "  A 
rational  reasoning  which  is  false  in  form  while  valid  in  appearance 
\  is  a  fallacy.  Such  a  reasoning  is  n.  paralogism  if  we  are  ourselves  de- 
ceived by  it.  It  is  a  sophism  if  we  seek  to  deceive  others." 9  Let  us 
define  more  widely,  and  say  that  any  violation  of  logical  law  is  a  fal- 
lacy. This  agrees  with  its  etymology  (fallere,  falsuin).  We  may 
have  fallacious  definitions  and  classifications  as  well  as  the  non  sequi- 
tur.  As  for  Kant's  subdivision,  it  is  not  logical,  but  psychological ;  one 
of  not  the  least  moment  in  Logic,  and  little  used  elsewhere.  Although, 
by  the  influence  of  Hamilton,  it  has  crept  into  our  language,  and  is 
repeated  by  nearly  all  subsequent  writers  on  Logic  with  humble  def- 
erence to  these  great  authorities,  we  shall  make  bold  to  discard  it,  and 
distinguish  paralogisms  and  sophisms  in  a  useful  logical  sense. 

Fallacies,  then,  are  of  two  kinds : 

1st.  Paralogisms;  or  those  whoso  violation  of  logical  law  is  manifest 
^upon  inspection  of  the  form  alone.  This  accords  pretty  nearly  with 
the  meaning  of  the  word  as  used  by  Aristotle.  It  is  so  used  by  De 
Morgan,  who  says:  "Paralogism,  by  its  etymology,  is  best  fitted  to 
signify  an  offence  against  the  formal  rules  of  inference."1  What 
here  we  call  paralogisms  are  distinguished  by  Whately  as  "  formal 
fallacies,"  and  by  Mill  as  "  fallacies  of  ratiocination." 

B  De  Sophistici  Elenchi,  ch.  ix.  The  full  title  of  this  treatise,  which  is  the  last  of 
the  series  constituting  the  ORGANON,  but  printed  by  Waitz  as  the  final  section  of 
the  Topica,  is  as  follows :  ITept  $e  T&V  <ro$>i<mfcwv  iXsy^wv  Kai  ~Cjv  tyaii'OiJ.evdii' 
Hiv  i\tyxwv  ovruv  St  TrapaXoyivn&v  d\\'  OVK  iXtvj^uv. 

9  Logik,  §  90.  lo  Formal  Logic,  p.  239. 


DISTRIBUTION.  257 

2d.  Sophisms ;  or  those  whose  violation  of  logical  law  is  not  mani- 
fest upon  inspection  of  the  form  alone,  but  requires  a  consideration 
of  the  language,  or  of  the  matter  to  discover  it.  These  correspond  in 
general  to  Whately's  "material  fallacies,"  and  to  Mill's  "fallacies  of™ 
confusion."  "It  answers  the  purpose  of  some  persons,"  says  Aris- 
totle, "rather  to  seem  to  be  philosophers  and  not  to  be,  than  to  be 
and  not  to  seem  ;  for  sophistry  is  seeming  but  unreal  philosophy,  and 
the  sophist  a  person  who  uses  the  semblance  of  philosophy  without 
the  reality."  That  is  to  say,  he  is  a  counterfeit  wise  man  (So</>oc, 
clever,  cunning).11 

Sophisms  are,  as  indicated  above,  subdivided  by  Aristotle  into  two 
classes,12  which,  in  the  terminology  of  the  Scholastics,  are  as  follows : 

(a)  Those  in  dictione,  or  in  voce  (01  napa  rt]v  \i£tv) ;  the  formal 
fault  being  concealed  by  ambiguity  of  language.     Generally,  there-   ' 
fore,  they  disappear  by  being  translated  from  one  language  into  an- 
other.    They  correspond  to  Bacon's  Idola  fori,  and  to  Whately's 

"  semi-logical  fallacies."  Of  them  Aristotle  makes  a  selection  rather 
than  a  division,  for  it  is  far  from  exhaustive,  of  six  classes,  which,  sub- 
sequently, we  treat  in  detail. 

(b)  Those  extra  dictionem,  or  in  re  (oi  t£w  rijQ  Ae&wc) ;  the  formal 
fault  lying  concealed  in  the  subject-matter.     Generally,  therefore,  as 
adhering  to  the  thought,  they  persist,  in  whatever  language  expressed. 
They  correspond  to  the  "  non-logical  fallacies"  of  Whately.     Of  them 
Aristotle  selects  and  treats  seven  kinds;  subsequently  considered. 

It  is  needful  to  forewarn  the  reader  that  fallacies  sometimes  present 
a  double  or  a  manifold  aspect,  one  view  bringing  them  under  one  class, 
another  under  another.  It  becomes,  in  such  case,  a  matter  of  doubt 
or  of  choice  to  which  genus  even  a  given  species  shall  be  referred. 
Very  often  the  same  individual  fallacy  may,  with  equal  propriety,  be 
referred  to  different  species,  and  sometimes  we  can  choose  whether  to 
regard  it  as  a  fallacy  or  not.  For  instance,  if  some  one  expatiates  on 
the  distress  of  a  country,  and  hence  argues  that  the  government  is 
tyrannical,  we  must  suppose  him  to  assume  either  that  "  Every  coun- 

11  Sir  Thomas  More  ( Works,  p.  475)  thus  caricatures  him :  "  A  Sophyster  woulde, 
with  a  fonde  argumente,  prove  unto  a  symple  soule  that  two  egges  were  three ;  be-  ^ 
cause  that  ther  is  one,  and  that  ther  be  twayne,  and  one  and  twayne  make  three. 
Yt  symple  unlearned  man,  though  he  lacke  learnying  to  soyle  hys  fonde  argumente, 
hath  yet  wit  enough  to  laugh  thereat,  and  to  eat  the  two  egges  himselfe,  and  byd  / 
the  Sophyster  tak  and  eat  the  thyrde." 

17 


258  OF    FALLACIES. 

try  under  a  tyranny  is  distressed,"  which  constitutes  the  fallacy  of  un- 
distributed middle;  or  that  "Every  distressed  country  is  under  a  tyr- 
anny," which,  though  materially  a  false  premise,  yields,  nevertheless, 
a  good  argument,  and  is  not  a  fallacy. 

The  foregoing  distribution  of  fallacies,  as  well  as  the  detailed  state- 
ment hereafter,  is  substantially  that  of  Aristotle.  He  has  been  followed 
closely  by  logicians  for  two  thousand  years,  the  only  considerable  mod- 
ification being  the  scholastic  terminology,  which  we  adopt.  Attempts 
at  an  improved  classification  have  been  made,  but  no  one  has  been 
generally  approved.  Mill's  arrangement  is  masterly,  but  in  the  de- 
partment of  deductive  fallacy  he  adheres  quite  closely  to  Aristotle. 
We  have  herein,  then,  nothing  new  to  present.  In  the  special  treat- 
ment, we  hope  to  show,  by  a  more  thorough  analysis,  that  the  several 
classes  are  amenable  to  the  laws  of  the  syllogism,  and  hence  are  strictly 
formal  fallacies.  The  classification  and  treatment  arc,  however,  far 
from  exhaustive.  The  ground  is  boundless.  No  'one  can  forecast  the 
devious  intricacies,  the  incoherences,  the  perplexities,  the  entanglements 
possible  to  the  human  understanding.  "  On  se  fait  une  idee  precise 
de  Pordre,  metis  non  pas  du  desordre" 

§  6.  Paralogisms,  as  we  have  termed  them,  were  not  treated  as  a 
class  of  fallacies  either  by  Aristotle  or  by  the  scholastics.  The  mas- 
ter, and  his  devout  disciples  until  very  recent  times,  were  so  perfectly 
familiar  with  the  laws  of  thought  and  their  application,  that  the  idea 
of  an  open  offence  against  the  formal  structure  of  a  proposition  or 
syllogism  being  unconsciously  committed  and  maintained  seemed  to 
them  impossible  and  absurd.  But  it  is  different  with  us.  Palpable 
violations  of  syllogistic  laws,  though  they  are  all  merely  laws  of  com- 
mon-sense, are  as  frequent  as  any  other  species  of  fallacy  whatever. 
The  slipshod  judgments  and  crippled  arguments  that  every -day  talk- 
ers, and  even  legislators,  preachers,  and  teachers,  are  sometimes  content 
to  use,  unconscious  of  their  utter  inconsequence,  greatly  need  to  be 
brought  into  the  sunlight  and  spread  out  in  thin  transparency.  But 
one  who  has  read  the  preceding  pages,  for  him  it  were  superfluous 
that  we  more  than  barely  indicate  these  bald  simplicities. 

A  paradox,  in  the  logical  sense,  is  a  self-contradiction.13  When  this 
is  manifestly  equivalent  to  A  =  non-A,  we  have  a  formally  fallacious 


13  This  is  the  sense  in  which  I  understand  Aristotle  in  general  to  use  the  word. 
See  De  Soph.  ch.  xii. 


DISTRIBUTION.  259 

judgment  or  a  contradictory  attribute.  Is  such  an  error  possible? 
When  a  speaker  begins  with  "  a  preliminary  remark,"  thus  "  referring 
to  what  he  is  about  to  say,"  we  are  reminded  of  a  schoolboy  "  back- 
ward in  his  progress,"  and  of  the  captain's  "  forward  march  to  the 
rear."  These,  of  course,  are  mere  blunders.  Fallacious  definitions  and 
divisions  have  been  sufficiently  illustrated  under  their  topics. 

Immediate  inferences  are  sometimes  fallaciously  drawn.  How  often, 
in  the  silence  of  thought,  if  not  orally,  is  this  error  committed :  All  , 
A  is  B ;  therefore,  all  B  is  A !  You  agree  with  me  that  to  possess  a 
large  amount  of  money  is  to  be  wealthy ;  then,  in  the  haste  of  talk,  I 
may  afterwards  say  you  just  now  admitted  that  to  be  wealthy  is  to 
possess  a  large  amount  of  money,  and,  unchallenged,  draw  a  false  con- 
clusion. The  difficulty  of  determining  whether  a  man  is  or  is  not  good 
is  a  commonplace  of  moralists  and  satirists.  Society,  however,  applies, 
without  hesitation,  a  very  simple  rule.  Since,  beyond  doubt,  good  men 
do  good  deeds,  it  concludes,  quite  satisfactorily  to  itself,  that  he  who 
does  good  deeds  is  a  good  man ;  whereas  selfish  prudence  dictates  a  / 
virtuous  course  of  action  almost  as  imperatively  as  virtue  itself.  We 
are  more  liable  to  this  error  because  so  many  universal  affirmatives 
are,  when  we  consider  the  matter,  simply  convertible ;  as,  "  Coin  is 
metallic  money."  Moreover,  though  "All  seed  come  from  plants,"  it 
does  not  logically  follow,  however  true  it  may  be,  that  "  All  plants 
come  from  seed." 

In  logical  opposition,  the  fallacy  of  using  the  contrary  of  a  proposi-/ 
tion,  instead  of  its  contradictory,  has  already  been  noticed.14  Impor- 
tant practical  errors  may  arise  from  this.  When  it  is  maintained,  as 
in  some  popular  creeds,  that  "  Every  dutiful  act  is  meritorious,"  this 
should  not  be  met  by  the  moralists  with  "  No  dutiful  act  is  meritori- 
ous,"— for  of  two  contraries  both  may  be  false, — but  with  "  Some 
dutiful  acts  are  not  so."  This  may  be  easily  proved ;  not  the  other, 
at  least  not  to  popular  apprehension.  That  a  thing  is  not  white  does  ,/• 
not  prove  it  black.  Nobody  can  commit  this  fallacy  thus  broadly 
stated;  but  in  the  intricacies  of  an  argument,  and  in  the  confusion  of 
many  words,  it  often  lies  in  wait  and  is  fatal.  Again,  when  I  affirm 
that  "  Some  are,"  my  opponent  ought  not  to  triumph  with  "  Some  are 
not ;"  for,  unless  it  be  the  same  "  Some,"  both  may  be  true.  Yet,  if 
he  artfully  frames  an  extended  reply,  the  people,  the  arbiters  in  all 
questions  not  strictly  personal,  will  very  likely  give  him  the  palm. 

"Part  3d,  ii,  §8. 


260  OF    FALLACIES. 

Paralogisms  violating  the  law  of  syllogism  have  already  been  suffi- 
ciently illustrated  in  connection  with  the  General  Rules.15  If  the 
several  propositions  of  a  syllogism  were  fully  stated,  these  paralogisms 
could  hardly  ever  occur;  but  since  almost  always  the  expression  is 
but  partial,  fallacy  may  lurk  unseen  in  the  unexpressed  thought.  The 
obvious  remedy  is  complete  statement. 

Another  paralogism  is  to  regard  the  conclusion  as  false  because  a 
premise  is  false,  or  because  the  argument  is  unsound  ;  also,  to  infer 
the  truth  of  a  premise  from  that  of  the  conclusion.  Thus,  if  some 
one  argues  for  the  existence  of  a  God  from  its  being  universally  be- 
lieved, another  might  perhaps  be  able  to  refute  the  argument  by  pro- 
ducing an  instance  of  some  nation  destitute  of  such  belief,  the  contra- 
dictory of  the  minor  premise ;  the  argument  ought  then  to  go  for 
nothing.  But  many  might  think  otherwise,  and  consider  that  this 
refutation  had  disproved  the  existence  of  a  God,  in  which  they 
would  be  guilty  of  an  illicit  process  of  the  major  term  ;  thus : 

Whatever  is  universally  believed  must  be  true ; 
The  existence  of  a  God  is  not  universally  believed ; 
.*.  The  existence  of  a  God  is  not  true. 

Others,  again,  from  being  already  convinced  of  the  truth  of  the  first 
conclusion,  the  existence  of  a  God,  would  infer  the  truth  of  the  prem- 
ise, which  would  be  the  fallacy  of  undistributed  middle ;  thus : 

What  is  universally  believed  is  true ; 
The  existence  of  a  God  is  true ; 
.'.  The  existence  of  a  God  is  universally  believed. 

If  these  two  fallacies  were  put  in  hypothetical  form,  the  one  would 
proceed  from  the  denial  of  the  antecedent  to  the  denial  of  the  conse- 
quent, the  other  from  affirming  the  consequent  to  the  affirmation  of 
the  antecedent.  These  two  conditional  fallacies,  which  have  been  al- 
ready pointed  out  under  a  previous  topic,  are,  therefore,  found  to  cor- 
respond respectively  with  those  of  illicit  process  and  undistributed 
middle.16 

16  See  Fart  4th,  i,  §  5.  16  Whately,  Logic,  p.  191. 


SOPHISMS    IN   DICTION.  261 


II.  SOPHISMS  IN  DICTION. 

§  1.  The  sophismce  in  dictione  are  those  that  require  an  inspection 
of  the  language  in  order  to  detect  the  formal  logical  fault.  They  all 
arise  from  ambiguities  of  expression.  A  term  repeated  ambiguously, 
though  identical  to  eye  and  ear,  must  be  counted  twice,  for  it  repre- 
sents two  different  concepts.  A  syllogism  containing  such  a  term  is, 
therefore,  in  thought,  a  Quatcrnio  terminorum,  or,  as  it  has  been  de- 
risively called,  a  logical  quadruped,  animal  quadrupes  logicum  (see 
General  Rules,  No.  1).  This,  fundamentally,  is  the  vice  of  all  fallacies 
in  dictione.  When  the  ambiguity  is  in  the  middle  term,  the  fallacy 
corresponds  very  nearly  with  that  of  undistributed  middle  ;  for  while 
in  ambiguous  middle  the  extremes  are  compared  with  two  different 
terms,  in  undistributed  middle  they  are  compared  with  two  different 
parts  of  the  same  term. 

We  enter  now  upon  the  consecrated  Aristotelic  ground,  and  must 
adhere  to  the  time-honored  terminology.  Aristotle  enumerates  and 
treats  six  kinds  of  these  sophisms,  of  which  we  adopt  the  following 
scholastic  designations. 


§   2.  The  first  class,  jffiquivocatio,  or  Homonymia   (o^uww/jm),  is  / 
ambiguity  in  a  single  term,  or  the  use  of  a  word  or  words  in  two 
different  senses.     If  this  is  the  middle  term,  we  have  the  sophism  of 
ambiguous  middle,  formally  a  quaternion.     For  example,  — 

All  criminal  actions  should  be  punished  by  law; 
Prosecutions  for  theft  are  criminal  actions  ; 
.*.  Prosecutions  for  theft  should  be  punished  by  law. 

The  middle  term  is  here  doubly  ambiguous,  both  ''criminal"  and 
"actions"  being  used  in  different  senses.  The  phrase  in  one  premise 
signifies  highly  injurious  deeds  ;  in  the  other,  a  legal  process.  Again  : 

Finis  rei  est  illius  perfcctio  ; 
Mors  est  finis  vitae  ; 
.*.  Mors  est  vitte  perfectio. 

Here  the  ambiguity  may  be  thrown  either  upon  the  finis  or  upon  the 
perfectio.  If  upon  the  latter,  we  have  ambiguous  major.  The  follow- 


262  OP    FALLACIES. 

ing  example  is  one  given  by  Aristotle  (ch.  iv),  redressed  by  Poste.  It 
is  taken  from  the  Euthydemus  of  Plato,  §  12-18.  The  middle  term, 
y/m/z/iamroc,  is  a  schoolboy  who  has  learned  to  spell.  The  minor 
term  is  ambiguous. 

6    JpafJtp,aTLKOQ    tTTlffrf]fJl(t)V' 


" 


o 
.'.  o  [ia.vQa.vwv 

Such  obvious  cases  as  these  would  of  course  deceive  no  one.  The 
scorn  with  which  logical  examples  are  often  treated  overlooks,  how- 
ever, the  fact  that  premises  in  actual  discussions  are  often  very  wide 
apart,  —  one  or  the  other,  indeed,  perhaps  not  stated  at  all,  —  and  the  con- 
clusion also  remote  ;  and  so  an  ambiguity  may  very  well  escape  detec- 
tion, and  lead  to  error.  "Whenever  we  can  bring  together  the  premises 
and  conclusion  in  the  form  of  a  compact  syllogism,  the  sophism  of 
equivocation  is  usually  quite  manifest.  We  must  recollect,  too,  that  a 
series  of  arguments  is  like  a  chain,  which  is  not  stronger  than  its 
weakest  link.  If  an  ambiguous  term  is  lurking  somewhere,  the  chain 
cannot  be  depended  on.  One  may  observe,  "  There  is  a  great  deal  of 
truth  in  what  has  been  said."  Yes,  maybe  it  is  all  true,  except  one 
essential  point.  The  sophistry  is  most  dangerous  that  lies  hidden  in 
minute  neglected  points.  "  Burglars  do  not,  in  general,  come  and 
batter  down  the  front  door;  but  climb  in  at  some  window  whose 
fastenings  have  been  neglected.  An  incendiary  does  not  kindle  a  tar 
barrel  in  the  middle  of  the  hall,  but  leaves  a  lighted  candle  in  the 
thatch  or  in  a  heap  of  shavings." 

Perhaps  no  fallacy  is  so  prolific  of  false  doctrine  as  this.  Are  mere 
words,  then,  so  dangerous  ?  "  Men  imagine,"  says  Bacon,  "  that  their 
minds  have  the  command  of  language;  but  it  often  happens  that 
language  bears  rule  over  their  minds."  And  this  rule  is  often  mis- 
rule. Living  languages,  especially,  abound  in  ambiguities,  and  no  pro- 
cedure is  safe  that  has  not  provided  against  them,  and  that  does  not 
lieep  close  watch  upon  them.  The  only  remedy  is  an  exact  definition 
and  a  consistent  use  of  terms.  Whoever  would  discuss  a  subject  in 
writing  or  speech  with  scientific  accuracy  must  set  out  with  defini- 
tions, and  often  state  the  precise  sense  in  which  he  uses  common 
words.  It  is  one  criterion  of  an  advanced  science  to  have  its  terms 
accurately  defined.  The  mathematical  and  physical  sciences  \vere  the 
first  to  make  progress  in  this  direction,  and  only  in  recent  times  have 
the  moral  sciences  thus  attempted  to  escape  vagueness  and  erroneous 
consequence. 


SOPHISMS    IN    DICTION.  263 

It  would,  perhaps,  be  impossible  to  enumerate  the  sources  or  kinds 
of  ambiguity  in  words,  or  the  errors  which  are  consequent  upon  it. 
Some  select  illustrations  must  suffice.  A  word  used  at  one  time  in  its 
etymological  or  primary  sense,  and  at  another  in  a  secondary  or  ac- 
quired and  perhaps  more  customary  sense,  yields  of  course  a  quater- 
nion. Thus  a  "  representative  "  being  originally  a  mere  spokesman, 
his  constituents  may  mistake  his  proper  function,  and  hold  him  a 
trust-breaker  if  he  uses  his  own  judgment  about  measures.  They 
might  as  rightly  insist  that  a  sycophant  is  merely  a  fig-shower.  So 
one  might  fancy  himself  safe  from  legal  penalties  for  "publishing  a 
libel,"  so  long  as  he  did  not  print  it.  Laws,  however,  do  not  travel  in 
meaning  with  their  words.  The  honor  of  a  discovery  is  usually  ac- 
corded to  him  who  first  publishes  it.  Hence  M.  Biot,  against  the  de- 
cision of  the  Royal  Society,  claimed  the  priority  in  the  discovery  of 
fluxions  for  Leibnitz  over  Newton,  because  of  a  private  letter  on  the 
subject  written  by  the  former  to  Oldenburg  in  1676,  which  was  prior, 
and,  in  the  legal  meaning  of  the  term,  a  publication.  Again,  the 
word  "to  utter,"  meaning  originally  "to  give  out,"  "to  issue,"  has 
changed  its  meaning.  No  one,  however,  under  indictment  for  "  the 
utterance  of  counterfeit  coin  "  would  be  likely  to  plead  in  defence 
that  nobody  ever  uttered  coin  except  the  princess  in  the  fairy  tale.1 

More  serious  errors  arise  from  the  customary  use  of  the  same  word 
in  various  senses.  The  word  "  nature  "  is  quite  ambiguous.  Butler 
pointed  out  three  meanings.  Sir  C.  G.  Lewis  makes  two  general 
classes  of  its  various  meanings:  1st,  a  positive  idea,  expressing  es- 
sence, quality,  or  disposition  ;  2d,  a  negative  idea,  excluding  art,  or  hu- 
man regulation  or  contrivance.  The  phrase  "  human  nature  "  is  used 
in  the  positive,  "  state  of  nature  "  in  the  negative  sense.  "  Every  man  , 
has  a  natural  right  to  his  liberty  "  is  a  jumble  of  uncertain  sounds. 

The  word  "moral "  is  variously  used.  It  seems  to  have  lost  entirely 
its  etymological  sense  (mos,  custom),  as  has  also  the  Greek  synonym 
"  ethical "  (i'jdos,  custom),  but  it  has  branched  out  into  various  meanings. 
It  is  opposed  to  physical  in  "  the  moral  and  physical  sciences,"  and  to 
demonstrative  in  "  moral  and  demonstrative  reasoning."  Even  in  the 
specific  sense  of  right  and  wrong  its  signification  fluctuates.  Accu- 
rately, its  criterion  is  law ;  a  moral  act  is  one  imposed  by  a  superior. 
Hence  when  we  speak  of  the  moral  governor  of  the  universe,  it  must 
be  understood  to  mean  merely  goodness  or  equity,  which  qualities 

lDe  Morgan,  p.  243. 


264  OF   FALLACIES. 

may  attach  to  a  supreme  legislator;  but  the  sovereign  has  no  moral 
duties ;  his  enactments  create  these  for  his  subjects. 

The  confusion  of  "  law  "  in  the  juridical  sense  with  "  law  "  as  a  uni- 
formity of  nature  is  exemplified  in  Butler's  chapter  on  "The  Moral 
Government  of  God."  He  calls  the  course  of  nature  a  government 
merely  on  the  ground  that  it  induces  precautions  to  avoid  pain.  But 
these  precautions  have  nothing  moral  in  them ;  they  may  be  used  for 
criminal  ends.  Guy  Fawkes  obeyed  a  law  of  nature  when  he  arranged 
for  firing  his  powder-mine  with  safety  to  himself.2 

The  several  meanings  in  which  the  word  "  inconceivable  "  is  used, 
and  its  confusion  with  "  incredible,"  have  obscured  greatly,  and  need- 
lessly extended,  the  controversy  between  the  intuitional  and  empirical 
schools  of  philosophy.  Antipodes  were  incredible  to  the  ancients,  but 
not  properly  inconceivable.  Every  child  conceives  clearly  that  "  the 
cow  jumped  over  the  moon,"  and  maybe  believes  it,  or  maybe  not. 
Necessary  truth  is  a  thing  conceivable,  the  contradictory  of  which  is 
inconceivable,  i.  e.,  cannot  be  thought  or  imaged  by  the  mind.  This 
contradictory  is  incredible ;  but  it  does  not  follow  that  whatever  is  in- 
^  conceivable  is  incredible.  Two  contradictories  may  be  equally  incon- 
ceivable, as  finite  and  infinite  space ;  but,  being  logical  contradictories, 
one  must  be  true.  Again,  before  the  coming  of  Christ,  it  was  inconceiv- 
able that  justice  and  mercy  could  consist,  but  not  incredible ;  since 
then  it  has  become  clearly  conceivable  also.  Now  it  is  inconceivable 
that  election  and  free-will  can  consist ;  but  these,  not  being  logical 
contradictories,  are  nevertheless  found  credible.8 

The  mercantile  public  frequently  commit  a  fallacy  by  the  ambigu- 
ity of  the  phrase  "  scarcity  of  money."  In  the  language  of  commerce, 
"money"  has  two  meanings, — currency,  or  the  circulating  medium, 
and  capital  seeking  investment,  especially  investment  on  loan.  In  this 
last  sense  the  word  is  used  when  the  "money  market"  is  spoken  of, 
and  when  the  value  of  money  is  said  to  be  high  or  low,  the  rate  of 
interest  being  meant.  The  consequence  of  this  ambiguity  is  that  as 
soon  as  the  scarcity  of  money  in  this  latter  sense  begins  to  be  felt,  as 
soon  as  there  is  a  difficulty  of  obtaining  loans,  and  the  rate  of  interest 
is  high,  it  is  concluded  that  this  must  arise  from  causes  acting  upon 


2  Bain's  Zo/7/c,  p.  617. 

8  The  troublesome  ambiguities  of  "  inconceivable "  are  discussed  by  Mill  in 
his  Examination  of  Hamilton,  ch.  vi ;  and  in  his  Logic,  bk.  ii,  chs.  v-vii.  He  argues, 
however,  in  the  interest  of  empiricism,  and  has  failed  to  dissipate  the  mists. 


SOPHISMS    IN    DICTION.  265 

the  quantity  of  money  in  the  other  and  more  popular  sense ;  that  the 
circulating  medium  must  have  diminished  in  quantity,  or  ought  to 
have  been  increased.  A  cry  then  arises  for  more  money,  for  more 
circulating  medium,  no  increase  of  which  can  possibly  relieve  this 
pressure.4 

When  St.  Paul  concludes  (Rom.  iii,  28)  that  "  A  man  is  justified 
without  the  deeds  of  the  law,"  he  is  using  the  word  "  justify  "  consist- 
ently throughout,  as  meaning  "  treated  by  God  as  free  from  guilt." 
When  St.  James  says  (Epist.  ii,  24),  "Ye  see  then  how  that  by  works 
a  man  is  justified,  and  not  by  faith  only,"  he  too  is  using  the  word 
consistently,  meaning  "  seen  to  be  just  before  God,"  which,  he  says, 
requires  the  evidence  of  works.  All  candid  minds  will  see  and  ac- 
knowledge that  in  such  a  case  the  two  statements  are  not  contradic- 
tory, and  that  both  arguments  are  conclusive.5 

The  paronomasia,  or  pun,  is  generally  the  logical  sophism  of  equivo- 
cation. Charles  Lamb6  quotes  the  following,  taken  from  Swift's 
Miscellanies :  "An  Oxford  scholar  meeting  a  porter  who  was  carrying 
a  hare  through  the  streets,  accosts  him  with  this  extraordinary  ques- 
tion :  Prithee,  friend,  is  that  thine  own  hare  or  a  wig  ?"  Lamb  com- 
ments on  this,  and  analyzes  the  fun  of  it  admirably.  The  Logic  of  it 
is  quite  plain.  The  enthymeme  implied  in  the  question  expands  thus : 

A  wig  is  not  one's  own  hair  ; 
Surely  that  is  not  your  own  hare ; 
.*.  It  must  be  a  wig. 

Here  are  two  negative  premises,  or  else  undistributed  middle,  as  well 
as  ambiguous  middle.  Still  we  may  say  that  a  pun  is  quite  generally 
a  mock  argument  founded  on  a  palpable  equivocation  of  the  middle 
term.  As  herein :  "  Two  men  ate  oysters  for  a  wager,  one  ate  ninety- 
nine,  but  the  other  ate  two  more,  for  he  ate  a  hundred  and  won." 
Here  the  reason  is  formally  proposed.  Virgil's  famous  line,7 
"  Mantua,  vae  miseroe  nimium  vicina  Cremonse !" 

contains  a  double  pun,  as  such  untranslatable  of  course,  but  may  be 
similarly  analyzed. 

It  may  be  well  to  remark  here,  once  for  all,  that  most  kinds  of 
witty  jests  are  mock  logic  of  some  sort.  Humor  seems  to  relate 
primarily  to  feeling,  feeling  exaggerated  or  misplaced.  Wit  relates 


4  Mill's  Logic,  p.  564.  6  McCosh's  Logic,  p.  176. 

6  Essays  of  Elia,  "  Popular  Fallacies,"  No.  ix.  '  Eclogue  ix,  28. 


266  OF   FALLACIES. 

rather  to  cognition,  is  more  intellectual  in  character,  and  often,  from 
under  a  logical  play  of  thought  manifestly  and  even  absurdly  falla- 
cious, lets  fly  a  sharp  dart  of  truth.  Dr.  Johnson's  fishing-pole,  "  a 
rod  with  a  worm  at  one  end  and  a  fool  at  the  other,"  is  a  mock  defini- 
tion. Mr.  Beecher's  jest,  "  People  are  the  good  people,  the  bad  peo- 
ple, and  the  Beechcrs,"  is  a  mock  division.  Artemus  Ward,  travelling 
on  a  railway -car,  suddenly  cries  out  in  alarm,  "Mister  Conductor, 
you've  put  the  cow-catcher  on  the  wrong  end  of  this  'ere  train  ;  there 
ar'nt  nothing  on  airth  to  prevent  a  cow  from  coming  right  in  behind 
here,  and  biting  the  folks."  Here  is  a  curious  mixture  of  humor  and 
sarcasm ;  humor  in  the  affected  alarm  at  the  supposed  mistaken  ar- 
rangement, and  the  grotesque  consequences  apprehended;  wit  in  the 
sly  assumption  "  Your  train  runs  slower  than  a  cow,"  implied  by  the  de- 
duction through  the  ambiguous  "  cow-catcher."  Even  the  most  seri- 
ously intended  sophism  becomes,  when  reduced  to  strict  logical  form, 
so  palpably  a  ludicrous  sham  that  we  wonder  any  one  could  be 
deceived  by  it.  As  majesty  stripped  of  its  externals  becomes  a  jest, 
so  many  a  grave  argument  may  be  exposed  to  laughter  and  contempt. 

§  3.  The  second  class,  Fallacia  amphibolice  (a/u<p*/3oXm),  differs  from 
V  the  last  in  that  the  ambiguity  lies  in  the  construction  of  a  sentence 
rather  than  in  a  term.  E.  g.,  How  much  is  twice  two  and  three?  I 
will  go  and  return  to-morrow.  I  hope  that  you  the  enemy  may  slay. 
A  member  of  the  House  of  Commons,  charged  with  having  called  an- 
other a  liar,  rose  and  said,  "  It  is  quite  true,  and  I  am  sorry  for  it." 
An  example  of  Aristotle's  is : 

TOVTO  o  opt!  TIQ  6p£ ' 
b  KIHJV  TOVTO  o  bpqi  Ti£' 

.*.  6  KlbiV  OjO£. 

The  major  premise  is  ambiguous.  Another  example  given  by  Aris- 
totle he  takes  from  the  Euthydemus,  §  67.8  A  disputant  says,  in  reply 
to  the  question  Is  the  speaking  of  the  silent  possible  ?  that  if  we  go 
by  a  factory  at  work,  we  shall  find  iron  tools  far  from  being  silent 
things.  This  furnishes  the  syllogism, 

The  speaking  of  iron  tools  is  possible ; 
The  speaking  of  iron  tools  is  the  speaking  of  the  silent ; 
.*.  The  speaking  of  the  silent  is  possible.     (Poste.) 

In  the  Nicene  Creed,  the  words  "  by  whom  all  things  were  made  "  are 
8  See  Jowett's  Plato,  vol.  i,  p.  205. 


SOPHISMS    IN    DICTION.  267 

grammatically  referable  either  to  the  Father  or  to  the  Son.  In  the 
Second  Commandment,  the  clause  "of  them  that  hate  me"  is  a  geni- 
tive governed  either  by  "  children  "  or  by  "  generation."  a 

When  a  sentence  has  thus  two  grammatical  renderings,  the  hearer 
is  likely  to  adopt  that  to  which  his  preference  inclines,  and  overlook 
the  other.  This  was  the  habitual  trick  of  the  oracles.  Thus  the 
prophecy  of  the  spirit  in  Henry  VI:10 

The  duke  yet  lives  that  Henry  shall  depose, 
But  him  outlive,  and  die  a  violent  death. 

But  this,  says  York,  is  just  the  famous  response  of  the  oracle  to 
Pyrrhus : 

Aio,  te,  JSacida,  Romanes  vincere  posse ; 

Ibis,  redibis  numquam  in  bello  peribis. 

§  4.  The  third  and  fourth  classes,  Fallacia  compositions  and  Fal- 
lacia  divisionis  (avvQeaiQ  and  dcatjpcarcc),  arise  from  the  confusion  of  ay 
universal  with  a  collective  term.  According  to  Whately,  when  a  dis- 
tributed term  is  afterwards  used  collectively,  it  is  the  fallacy  of  compo- 
sition ;  when  a  collective  term  is  afterwards  used  distributively,  it  is 
the  fallacy  of  division.  This  is  clear,  but  seems  not  to  have  been  ex- 
actly the  meaning  of  Aristotle,  and  the  distinction  is  hardly  worth 
preserving.  Aristotle's  example  is  as  follows : 

Two  and  three  (distributively}  are  even  and  odd ; 
Two  and  three  (collectively}  are  five ; 
/.  Five  is  even  and  odd. 

The  ambiguity  of  " all"  has  been  repeatedly  noticed.  When  taken 
at  one  time  in  its  cumular,  at  another  in  its  exemplar  or  distributive 
sense,  it  gives  rise  to  this  sophism.  E.  g. : 

All  the  angles  of  a  triangle  are  equal  to  two  right  angles ; 
A  B  C  is  an  angle  of  a  triangle : 
.'.  A  B  C  is  equal  to  two  right  angles. 

So  "  All  these  trees  make  a  thick  shade  "  may  mean  either  that  all 
together  do  so,  or  that  each  does  so.  AVhen  a  multitude  of  particu- 
lars are  presented  to  the  mind,  many  persons  are  too  weak  or  too  in- 

9  One  more  notable  amphiboly :  "  All  the  dormitories  of  this  university  shall 
be  occupied  by  two  students  except  nine,  they  being  single."     (Old  Regulations.) 
"  Two  students  shall  occupy  every  room  in  this  university  except  nine,  and  one 
student  shall  occupy  these."     (Revised  Code.) 

10  Part  2,  act  i,  sc.  iv. 


268  OF    FALLACIES. 

dolent  to  take  a  comprehensive  view  of  them  ;  but  confine  their  at- 
tention to  each  by  turns,  infer,  decide,  and  act  accordingly.  Thus,  the 
debauchee  destroys  his  health  by  successive  acts  of  intemperance,  be- 
cause no  one  of  these  acts  would  of  itself  be  sufficient  to  destroy  it. 
Others  reason  thus:  I  am  not  bound  to  contribute  to  this  charity, 
nor  to  that,  nor  to  the  other,  drawing  the  practical  conclusion  that  all 
charity  may  be  neglected.11  The  Owenites  are  said  to  reason  thus 
against  the  doctrine  of  human  responsibility  : 

He  who  necessarily  goes  or  stays  is  not  a  free  agent  ; 
But  every  one  necessarily  either  goes  or  stays  ; 
.*.  No  one  is  free. 

All  such  reasonings  are  obviously  quaternions. 

We  sometimes  hear  an  argument  to  prove  that  the  world  could  do 
very  well  without  great  men.  If  Columbus  had  never  lived,  America 
would  still  have  been  discovered,  at  most  only  a  few  years  later  ;  if 
Newton  had  never  lived,  some  other  person  would  have  discovered  the 
law  of  gravitation,  etc.  Granted,  but  probably  not  until  some  one 
arose  having  the  qualities  of  Columbus  and  of  Newton.  Because 
any  one  great  man  might  have  had  his  place  supplied  by  another 
great  man,  the  argument  concludes  that  all  great  men  could  be  dis- 
pensed with.  The  term  "great  men"  is  distributive  in  the  premises, 
and  collective  in  the  conclusion.12 

t         §  5.  The  fifth  class  is  Fallacia  prosodies,  or  accentus 
*  An  example  given  by  Aristotle  is  from  Homer  : 


v  KarcLTrvQiTcn  o[i(3p<p.1* 

Some  critics,  he  says,  emend  tbis,  speaking  the  ov  more  sharply 
(XeyovTEQ  TO  ov  oZvTepov),  changing  affirmative  to  negative;  instead 
of  "  part,"  saying  "  naught  is  rotten  by  the  rain."  He  prefaces  this  by 
the  remark  that  the  ambiguity  can  hardly  occur  in  speech,  but  only  in 
writing.  This  is  because  in  his  time  the  written  words  of  the  Greeks 
were  not  marked  with  accents  and  breathings,  and  hence  were  some- 
times ambiguous  to  the  eye  when  not  to  the  ear. 

In  like  manner  with  us  an  ambiguity  in  a  written  word  or  phrase 
is  resolved  usually  by  a  stress  in  voce.  Thus,  gallant,  brave  ;  and 
gallant',  courteous.  "  Not  the  least  difference  "  may  mean  either  no 
difference  at  all,  or  a  very  considerable,  perhaps  the  greatest,  difference. 

11  Whately,  p.  217.          "  Mill,  p.  570.          1S  Iliad,  23,  328.    Dindorf  has  ov. 


SOPHISMS    IN    DICTION.  269 

If  in  reading  "  Thou  slialt  not  bear  false  witness  against  thy  neigh- 
bor," the  last  word  is  emphasized,  we  convey  the  meaning  that  per- 
jury is  not  forbidden  except  against  the  neighbor.  We  read  in  the 
first  book  of  Kings,  xiii,  27,  "And  the  prophet  spake  to  his  sons, 
saying,  Saddle  me  the  ass ;  and  they  saddled  him"  The  italics  indicate 
that  the  word  was  supplied  by  the  translators;  mistaking  it  for  an 
emphatic  word  transfers  the  saddle.  Jeremy  Bentham,  it  is  said,  so 
feared  being  misled  by  false  accent  that  the  person  employed  to  read 
for  him  was  required  to  maintain  a  monotone. 

The  fashion  of  taking  a  Scripture  text  and  drawing  thence  a  series 
of  doctrines  by  putting  emphasis  first  on  one  word  and  then  on  an- 
other is  very  questionable,  if  not  dangerous.  A  wrong  emphasis  may 
pervert  and  wholly  confound  the  meaning.  But,  on  the  other  hand, 
we  may  by  admissible  and  various  emphasis  forcibly  present  different 
views  of  the  same  sentiment.  Observe  in  what  different  lights  the 
thought  may  be  placed  by  changing  the  stress  of  voice  on  the  words 
of  our  Saviour :  Judas,  betrayest  thou  the  Son  of  man  with  a  kiss  ! 

Bdraycst  thou, — makes  the  reproach  turn  on  the  infamy  of  treachery. 
Betrayest  tliou, — makes  it  rest  upon  Judas's  connection  with  his  Master. 
Betrayest  thou  the  Son  of  man, — rests  it  upon  the  Saviour's  personal  character. 
Betrayest  thou  the  Son  of  man  with  a  kiss  ! — turns  it  upon  his  prostitution  of  the 
sign  of  friendship  and  peace  to  a  mark  of  hate  and  ruin. 

Any  statement  of  something  that  has  been  said  with  a  suppression 
of  such  tone  as  was  meant  to  accompany  it  is  the  fallacy  of  accent. 
Gesture  and  manner  may  easily  make  all  the  difference  between  truth 
and  falsehood.  A  person  who  quotes  another,  omitting  anything 
which  serves  to  show  the  animus  of  the  meaning;  or  one  who  with- 
out notice  puts  any  word  of  the  author  he  cites  in  italics  so  as  to 
alter  its  emphasis;  or  any  one  who  attempts  to  heighten  his  own  as- 
sertions, so  as  to  make  them  imply  more  than  he  would  openly  avow, 
by  italics,  or  notes  of  exclamation,  or  otherwise,  is  guilty  of  F.  ac- 
centus.  We  have  said  that  jests  are  generally  fallacies.  Sarcasm  and 
irony  may  be  referred  to  the  fallacy  of  accent,  perhaps  cannot  be  as- 
sumed without  it.  Some  one,  it  may  be,  declines  a  task  as  beyond  his 
powers;  and  another  assures  him  that  his  diffidence  is  highly  com- 
mendable, and  fully  justified  by  the  circumstances.  Said  Job  to  his 
friends,  No  doubt  but  ye  are  the  people,  and  wisdom  shall  die  with 
you; — meaning  the  contrary.  The  tones  and  inflections  of  his  voice, 
we  may  feel  sure,  were  those  peculiar  to  irony.  This  is  very  effective, 
since  it  is  hardly  possible  to  frame  a  reply. 


270  OF    FALLACIES. 

§  6.  The  sixth  class,  Fallacia  figurce  dictionis  (or^j/yua  Xt^fwe),  was 
limited  by  Aristotle  to  the  using  of  words  having  similar  termina- 
tions; to  cases  wherein  unlike  things  have  names  with  like  inflection. 
The  name  of  what  is  not  an  action,  he  says,  may  terminate  like  the 
name  of  an  action  (e.  g.,  ailm^  and  cuttm^),  and  give  ground  for 
sophistry.  This,  however,  is  hardly  possible  in  uninflected  languages, 
and  so  at  present  the  species  is  commonly  held  to  include  any  perver- 
sion of  grammar,  any  solecism.  For  example  : 

Whatever  a  man  walks  on  he  tramples  on ; 
This  man  walks  on  the  whole  day ; 
/.  He  tramples  on  the  day. 

Very  similar  to  this  source  of  ambiguity  is  that  arising  from  the 
use  of  paronyms,  or  conjugate  words,  such  as  a  substantive,  adjective, 
and  verb  coming  from  the  same  root.  These  have  by  no  means  sim- 
ilar meanings.  E.g.,  "Artist,  artisan,  artful;"  "Pity  and  pitiful;" 
"Presume  and  presumption;"  "Project  and  projector;"  What  is 
"imaginary"  is  unreal,  but  an  "image"  formed  of  wood  or  stone  is 
real ;  To  "  apprehend  "  is  to  lay  hold  on,  or  to  come  to  a  knowledge 
of,  while  "  apprehension  "  often  signifies  fear  or  dread. 

Designing  persons  are  untrustworthy ; 

Everybody  forms  designs ; 
.*.  Nobody  can  be  trusted. 

Are  there  people  in  the  world  foolish  enough  to  think  that  strong 
drink,  because  it  is  strong,  gives  strength  ?  Then  they  commit  the 
double  fallacy  of  ambiguous  terms,  and  of  supposing  that  an  effect 
must  be  like  its  cause.  They  should  try  strong  poison.  Fallacies 
founded  on  such  differences,  says  Whately,  can  hardly  be  more  than 
jests. .  They  are  not  named  by  Aristotle,  because  in  Greek,  a  more 
regularly  constructed  language,  the  meaning  of  paronyms,  with  very 
few  exceptions,  does  exactly  correspond ;  and  paronyms  (ra  ffvaroL-^a) 
were  a  locus  of  dialectic,  i.  e.,  of  valid,  reasoning.14 

The  literal  construction  of  metaphors  and  other  figures  of  speech 
is  also  to  be  included  under  figura  dictionis  ;  e.  g. : 

Herod  is  a  fox ; 
A  fox  is  a  quadruped ; 
.'.  Herod  is  a  quadruped. 

In  giving  this  example,  Hamilton's  patience  breaks  down.    Disgusted 

14  See  Topica,  ii,  ch.  ix.  "  Si  Ton  a  demontre  que  I'un  des  conjugues  est  bon  ou 
qu'il  est  mauvais,  on  aura  demontre,  par  cela  meme,  que  tous  les  autres  le  sont 
egalement." — St.-IIilaire. 


SOPHISMS    IN    DICTION.  271 

with  these  trifling  distinctions,  he  says  that  Sophismata  equivocationis, 
amphibolies,  et  accentus  may  easily  be  reduced  to  Sophisma  figures 
dictionis ;  "  they  arc  only  contemptible  modifications  of  this  con- 
temptible fallacy."  J  But  when  we  remember  that  figurative  expres- 
sions are  more  natural  and  usual  than  literal  speech,  especially  if  the 
subject  be  important  and  interesting ;  that  a  matter  entirely  new  can 
hardly  be  discussed  or  even  spoken  of  except  metaphorically  ;  that  the 
history  of  the  moral  sciences  shows  how  difficult  it  is  to  avoid  being 
misled  by  material  conceptions,  which  are  not  even  analogous,  but 
only  remotely  comparative;  and  that  in  debate  illustrations  are  con- 
stantly mistaken  for  arguments,  and,  if  brilliant,  dazzle  the  vision,  and 
exert  more  convincing  and  persuasive  power  than  the  most  solid  logic ; 
we  may  rightly  conclude  that  the  sophism  figura  dictionis,  so  far  from 
being  contemptible,  is  worthy  of  our  closest  and  most  watchful  con- 
sideration. 

The  great  stress  laid  by  Aristotle  and  his  early  followers  on  so 
many  different  forms  of  verbal  deception,  what  now  we  should  call  a 
mere  quibble,  may  have  arisen,  says  De  Morgan,16  from  the  tendency 
in  early  times  to  place  undue  force  on  the  verbal  form  of  engage- 
ments and  admissions,  independently  of  the  understanding  with  which 
they  were  made.  Jacob  was  allowed  to  keep  the  blessing  which  he 
obtained  by  a  trick ;  Dido  surrounded  the  site  of  Carthage  with  strips 
of  the  ox-hide;  Lycurgus  seemed  fairly  to  have  bound  the  Spartans 
to  follow  his  laws  until  his  return,  though  he  intimated  only  a  short 
absence,  and  made  it  eternal ;  and  the  Hindoo  god,  who,  in  the  shape 
of  a  dwarf,  begged  a  realm  of  three  steps,  and  then,  in  shape  of  a 
giant,  took  earth,  sea,  sky,  seems  to  have  been  considered  as  claiming 
no  more  than  was  granted.  But,  nowadays,  one  undertaking  to  cross 
a  bridge  in  an  incredibly  short  time,  and  then  crossing  it  as  we  cross 
a  street,  would  hardly  be  held  as  having  fulfilled  his  engagement. 

16  Logic,  p.  327.  "  Logic,  pp.  244,  246. 


OF    FALLACIES. 


III.  SOPHISMS  IN  MATTER. 

§  1.  The  Sophismata  extra  dictioncm  are  those  in  which  we  must  go 
beyond  the  outer  form  and  beyond  the  diction,  and  inspect  the  matter 
of  thought,  in  order  to  discover  the  logical  fault.  They  are  common- 
ly called  "Material  Fallacies,"  and  described  as  those  whose  fault  does 
not  lie  in  form  nor  in  language,  but  in  the  matter,  meaning  by  this 
that  the  form  is  correct,  but  that  the  premises  are  false.  If  so,  then 
they  are  logically  faultless,  and,  as  already  said,  their  consideration 
does  not  belong  to  our  subject.  But  it  is  not  so ;  these  sophisms  are 
logically,  formally  faulty ;  only  it  is  requisite  that  we  examine  the 
matter  in  order  to  discover  this.  Of  this  genus,  Aristotle,  and  after 
him  the  Latin  logicians,  enumerated  seven  species,1  as  follows : 

The  first  class,  Fallacia  accidentis  (rrapa.  TO  (rvpfitfiriKog),  arises,  says 
^  Aristotle,  from  the  equation  of  subject  and  accident,  or  whenever  it  is 
assumed  that  subject  and  accident  have  all  their  attributes  in  common. 
By  "  accident"  here  (erv^ftfftriKoq  as  opposed  to  ovaia)  Aristotle  means, 
not  merely  what  is  usually  called  the  accident  in  Logic,  but  any  subor- 
dinate part  of  a  general  notion.  Every  species  and  individual  is  to  be 
regarded  as  an  accident  of  its  genus  in  this  sense.2  For  example, 
"  All  men  (subject)  are  mortal ;  but  Every  horse  is  (an  accident  of) 
mortal ;  hence  (equating  subject  and  accident),  Every  horse  is  a  man, 
and  Every  man  is  a  horse."  But  it  does  not  follow  that  "man"  and 
"horse"  have  all  their  attributes  in  common.  An  example  from  the 
text  is :  "  Since  Coriscus  is  not  Socrates,  and  Socrates  is  a  man,  it  does 
not  follow  that  Coriscus  is  not  a  man,  because  Socrates,  who  is  de- 
nied of  Coriscus,  is  merely  an  accident  of  .man."  Obviously  these 
examples  are,  the  one  undistributed  middle,  the  other  illicit  major ; 
but  as  illustrations  of  the  present  sophism  we  must  take  a  differ- 
ent view  of  them.  Either  premise  of  the  first  and  the  major  of  the 
second  are  supposed  to  be  converted  simply,  instead  of  per  accidens. 

1  De  Soph.  ch.  v.  Aristotle  does  not  consider  these  sophisms  as  having  false 
premises,  but  exposes  in  detail  their  formal  faults.  He  repeatedly  excludes  from 
Logic  the  consideration  of  matter  as  true  or  false. 

*  See  De  Soph.  ch.  xxiv,  where  Accidens  is  discussed  at  greater  length. 


SOPHISMS    IN    MATTER.  273 

This,  if  legitimate,  would  give  Barbara  and  Camestres,  but,  being  ille- 
gitimate, gives  rise  to  the  F.  accidentis.  Another  example  from  the 
text  is  as  follows: 

You  do  not  know  what  I  am  going  to  ask  you  about ; 
I  am  going  to  ask  you  about  the  nature  of  the  summum  bonum; 
.".  You  do  not  know  the  nature  of  the  summum  bonum. 

Here  the  subject  (unknown)  of  the  genus  (about  to  be  asked)  is  equated 
with  its  accident  (summum  bonum).  The  example  may  be  viewed  as 
undistributed  middle,  or  still  more  properly  as  an  amphiboly. 

We  are  now  enabled  to  classify  certain  sophisms  which  have  long 
been  lying  loose  in  our  Logics.  The  standard  example  is : 

He  who  calls  you  a  man  speaks  truly ; 
He  who  calls  you  a  knave  calls  you  a  man ; 
/.  He  who  calls  you  a  knave  speaks  truly. 

Here  is  inferred  of  a  subject  naming  a  species  (knave)  what  is  pre- 
mised of  a  subject  naming  a  genus  (man).  This  is  the  best  solution  I 
have  seen,  but  it  is  not  thereby  brought  under  any  Aristotelic  class. 
De  Morgan  confesses  it  troublesome,  and  concludes  it  is  best  consid- 
ered Equivocation.3  But  it  is  clearly  Aristotle's  F.  accidentis.  Thus : 
"  You  (subject)  are  a  man  (genus) ;  but  A  knave  is  (an  accident  of)  a 
man ;  therefore  (equating  subject  and  accident)  You  are  a  knave." 
Or  else,  evidently,. undistributed  middle. 

The  name  given  to  the  legitimate  conversion  of  A  by  Boethius4 
confirms  this  explanation  of  Aristotle's  meaning.  He  has  been  very 
generally  and  very  variously  misunderstood,  so  that  practically  this 
species  of  sophism  has  long  since  dropped  out  of  the  list.  Indeed, 
there  are  very  few  logicians  who  treat  it  correctly,  or  seem  even  to 
understand  it.  Errors  arising  from  this  malconversion  have  already 
been  indicated  in  i,  §  6,  on  Paralogisms. 

§  2.  The  second  class,  Fallacia  a  dicto  secundum  quid  ad  dictum 
simpliciter  (TO  a.7r\wQ  f/  fji>i  a7rXd>c  uAAa  Try  T)  TTOV  >/  TTOTE  >/  Trpog  n 
Xeyevdai),  arises  from  the  confusion  of  an  absolute  statement  with  a 
statement  limited  in  manner,  place,  time,  or  relation.  It  is  obvious 
that  this  includes  the  correlative  Fallacia  a  dicto  simpliciter  ad  dictum 
secundum  quid.  This,  beyond  question,  was  the  intent  of  Aristotle ; 
but  Whately,  followed  by  De  Morgan,  Mill,  Bain,  and  their  seconda- 

8  Logic,  p.  242.  4  Tart  SJ,  ii,  §  7. 

13 


274  OF    FALLACIES. 

ries,  identifies  the  latter  with  F.  accidentis,  which,  in  the  Aristotelic 
sense,  is  ignored.  It  is  needless  to  make  separate  species  of  these 
correlatives.6 

The  first  infers  from  a  statement  made  under  a  restriction  (secun- 
dum  quid)  to  one  made  without  restriction  (rimpliciter).  E.  g. : 

Whatever  is  pernicious  ought  to  be  forbidden ; 
The  use  of  wine  is  pernicious ; 
.'.  The  use  of  wine  ought  to  be  forbidden. 

Here  the  minor  premise  refers  to  wine  used  immoderately ;  the  con- 
clusion, to  wine,  however  used.  This  is  the  time-honored  sophism  of 
arguing  against  a  thing  from  the  abuse  of  it. 

The  second  infers  from  a  statement  made  without  limitation  to  one 
limited,  proceeding  from  what  is  essential,  it  may  be,  to  what  is  acci- 
dental.6 The  old  standard  example  is : 

What  you  bought  yesterday  you  ate  to  day ; 
You  bought  raw  meat  yesterday ; 
.'.  You  ate  raw  meat  to-day.7 

Here  is  inferred,  in  the  conclusion,  of  meat  with  the  accidental  quality 
of  rawness  added,  what  in  the  major  is  said  of  it  simply  ;  i.  e.,  of  the 
essential  substance,  without  regard  to  its  accidental  qualities. 

The  first  of  these  cases,  when  we  look  into  the  matter,  may  evident- 
ly be  construed  as  illicit  minor ;  for  what  is  premised  of  some,  a  cer- 
tain use  of  wine,  is  concluded  of  all  use  of  wine.  The  second  case  is 
plainly  a  quaternion,  having  an  ambiguous  middle ;  for  "  What  you 
bought  yesterday"  is  used  in  two  different  senses, — first  simply  or  es- 
sentially only,  secondly  with  its  accident. 

Under  this  class  of  sophisms  might  be  included  one  to  be  called 
F.  a  dicto  secundum  quid  ad  dictum  secundum  alterum  quid.  When 
it  is  asserted  that  the  desire  of  a  sportsman  to  take  life  is  cruel  and 
despicable,  to  answer  that  those,  also,  who  eat  flesh  from  which  life 
has  been  taken  by  others  have  therefore  cruel  and  despicable  desires 
is  to  infer  from  one  special  case  to  another  special  case,  and  is  the 
sophism  named.8 

6  See  De  Soph.  ch.  xxv.          6  Hence,  perhaps,  the  confusion  with  F.  accidentis. 

7  "  This  piece  of  raw  meat  has  remained  uncooked,  as  fresh  as  ever,  a  prodigious 
time.     It  was  raw  when  Reisch  mentioned  it  in  the  Margurita  Philosopliica,  in 
1496;  and  Whately  found  it  in  just  the  same  state  in  1826." — De  Morgan,  p.  251. 

8  De  Morgan,  p.  2C5. 


SOPHISMS    IN    MATTER. 

Perhaps  the  commonest  and  most  dangerous  sophisms  of  the  species 
now  before  us  are  those  which  do  not  lie  in  a  single  syllogism,  but  slip 
in  when  passing  from  one  syllogism  to  another  in  a  chain  of  argu- 
ment, and  are  thus  committed  by  changing  the  premises.  One  of  the 
conditions  oftenest  changed  is  the  qualification  of  time.  It  is  a 
principle  in  political  economy  that  prices,  profits,  wages,  etc.,  "  always 
find  their  level."  This  is  often  interpreted  as  if  it  meant  that  they 
are  most  generally  at  their  level,  while  the  truth  is  they  rarely  are, 
but,  as  Coleridge  expresses  it,  "  they  are  always  finding  their  level," 
which  might  be  taken  as  a  paraphrase  or  an  ironical  definition  of  a 
storm. 

It  is  a  very  good  rule  not  to  encourage  beggars,  but  we  should  not 
infer  of  all  who  solicit  alms  what  is  true  only  of  professional  beggars. 
So,  also,  it  is  a  good  general  rule  to  avoid  lawsuits,  but  sometimes  cir- 
cumstances make  an  appeal  to  law  a  duty.  These  may  be  taken  as  in- 
stances of  the  error  vulgarly  called  the  misapplication  of  abstract  truth ; 
that  is,  where  a  principle,  true  in  the  abstract,  is  applied  to  concrete 
cases,  and  reasoned  on  as  if  it  were  true  absolutely,  and  no  modifying 
circumstances  could  ever  by  possibility  exist.  This  is  to  reason  a  dicto 
simplidter  ad  dictum  secundum  quid.  It  is  an  error  very  common 
and  very  fatal  in  politics  and  society.9 

It  is  by  this  fallacy  that  orators  and  devotees  deceive  others,  and 
are  themselves  deceived,  while  they  use  the  words  loyalty,  authority, 
liberty,  faith,  religion.  The  essence  of  these  noble  qualities  is  con- 
founded with  their  accidents.  Men  commend  a  loyalty  to  a  person 
which  is  disloyalty  to  a  nation  ;  obedience  to  a  power  which  has  no 
rightful  authority ;  a  liberty  which  is  licentiousness ;  a  faith  which  is 
mere  credulity ;  a  religion  which  is  superstition.10 

The  gods,  say  the  Epicureans,  must  be  invested  with  human  form, 
because  that  form  is  most  beautiful,  and  everything  beautiful  must  be 
found  in  them.  But  as  the  human  form  is  not  absolutely  beautiful, 
but  only  in  relation  to  other  bodies,  it  does  not  follow  that  it  must  be 
in  God,  who  is  beautiful  absolutely.11 

The  law,  especially  in  criminal  cases,  requires  a  degree  of  accuracy 
in  stating  the  secundum  quid  which  to  many  persons  seems  absurd. 
A  man  indicted  for  stealing  a  ham  was  acquitted  on  the  ground  that 
the  evidence  showed  only  that  he  had  stolen  a  part  of  a  ham.  An- 
other being  convicted  of  perjury  committed  "in  the  year  1846,"  the 

9  Mill's  Logic,. p.  562.  10  McCosh's  Logic,  p.  128.  Il  Arnauld,  p.  262. 


276  OF    FALLACIES. 

judge  entertained  the  objection  of  the  counsel  that  it  ought  to  have 
read  "  in  the  year  of  our  Lord  1846."  ia  Such  minutiao  are  denounced 
as  "  the  quibbles  and  quirks  of  the  law  ;"  but  abundant  experience 
has  shown  that  the  most  minute  caution  is  requisite  not  to  commit 
injustice  through  the  fallacy  of  secundum  quid. 

We  recur  again  to  the  statement  that  jests  are  usually  palpable  fal- 
lacies. Boccaccio  tells  the  following  story  :  "  A  servant  who  was  roast- 
ing a  stork  for  his  master  was  prevailed  upon  by  his  sweetheart  to 
cut  off  a  leg  for  her  to  eat.  When  the  bird  came  upon  the  table,  the 
master  desired  to  know  what  was  become  of  the  other  leg.  The  man 
answered  that  storks  never  had  but  one  leg.  The  master,  very  angry, 
but  determined  to  strike  his  servant  dumb  before  he  punished  him, 
took  him  the  next  day  into  the  fields,  where  they  saw  storks  standing 
each  on  one  leg,  as  storks  do.  The  servant  turned  triumphantly  to 
his  master,  on  which  the  latter  shouted,  and  the  birds  put  down  their 
other  legs,  and  flew  away.  4  Ah,  sir,'  said  the  servant,  '  but  you  did 
not  shout  to  the  stork  at  dinner  yesterday  ;  if  you  had  done  so,  he 
would  have  shown  his  other  leg  too.'  "  The  gist  of  this  is  in  the  as- 
sumption that  what  can  be  predicated  of  storks  in  general  can  be 
predicated  of  roasted  storks  ;  a  dicto  simpliciter  ad  dictum  secundum 
quid.  And  so  when  the  calculating  boy,  Zerah  Colburn,  was  asked 
how  many  black  beans  it  would  take  to  make  ten  white  ones,  he 
promptly  replied,  "Ten,  if  you  skin  'em."  A  worthy  reply.  A  bean 
stripped  of  its  accidents  is  still  a  bean. 


§  3.  The  third  class,  Ignoratio  elenchi  (TO  Trapa  T^V  rov 
en-),  is  ignorance  of  the  refutation,  answering  to  the  wrong  point,  prov- 
ing something  not  the  contradictory  (elenchus)  of  the  thesis  which  one 
intends  to  overthrow.  This  supposes  a  disputant,  an  attempt  at  con- 
futation, and  is  the  view  to  which  Aristotle  limited  his  treatment.  It 
is  usual  now  to  take  a  wider  view,  and  under  the  more  general  title, 
proposed  by  Whately,  of  Irrelevant  Conclusion,  or  mistaking  the  issue, 
to  include  all  cases  where  the  attempt  is  to  establish  a  thesis  by  a 
proof  of  something  not  sustaining  it,  or  of  something  which  may  be 
mistaken  for  it.  This  latter  might  well  be  termed  Ignoratio  or  Mutatio 
condusionis.  Formally  the  fault  is  either  in  establishing  something 
that  is  not  the  required  contradictory  of  the  thesis,  or  else  establishing 
something  that  is  not  the  required  thesis. 

"  For  a  discussion  of  these  two  cases,  sec  De  Morgan,  p.  252  sq. 


SOPHISMS    IN    MATTER.  277 

If  I  argue  the  general  utility  of  some  proposed  measure,  and  my 
opponent  offers,  in  confutation,  proof  that  we  are  not  specially  interest- 
ed in  it,  he  ignores  the  true  elenchus,  and  his  conclusion  is  irrelevant. 
If,  in  support  of  my  thesis,  I  show  that  it  is  the  proper  consequence 
of  previous  legislation,  I  ignore  the  true  conclusion,  and  my  conclusion 
is  irrelevant.  If  it  be  affirmed  that  a  man  has  a  right  to  dispose  of 
his  property  as  he  thinks  best,  and  you  attempt  to  refute  by  showing 
that  the  way  he  has  adopted  is  not  the  best ;  if  one  party  vindicates, 
on  the  ground  of  general  expediency,  a  particular  instance  of  resistance 
to  government,  and  you  oppose  that  we  ought  not  to  do  evil  that 
good  may  come,  you  are  guilty  in  each  case  of  ignoratio  elenchi. 
Again,  if,  instead  of  proving  that  the  prisoner  has  committed  an  atro- 
cious crime,  you  prove  that  the  crime  of  which  he  is  accused  is  atro- 
cious ;  if,  instead  of  proving  that  the  poor  ought  to  be  relieved  in  this 
way  rather  than  that,  you  prove  that  the  poor  ought  certainly  to  be 
relieved,  you  are  guilty  in  each  case  of  ignoratio  condusionis.  The 
special  pleadings,  technically  so  called,  in  our  courts  of  law  previous 
to  trial  are  intended  to  produce,  out  of  the  varieties  of  statement 
made  by  the  parties,  the  real  points  at  issue,  so  that  the  case  may  not 
be  ignoratio  conclusionis,  nor  the  defence  ignoratio  elenchi.  "A  de- 
murrer" is  about  equivalent  to  the  remark  "Well,  what  of  that?" 
That  is,  granting  the  statement  in  question,  it  may,  perhaps,  be  no 
ground  of  action,  and,  if  so,  is  irrelevant. 

Nothing  can  be  more  important  in  the  construction  and  prosecution 
of  an  argument  than  a  clear  and  adequate  conception  of  the  precise 
point  to  be  proved  or  disproved.  In  the  speech  of  Diodotus13  in  an- 
swer to  Cleon,  who  had  argued  that  it  would  be  just  to  put  the  Mity- 
lenians  to  death,  he  reminds  him  that  the  question  was  not  that,  but 
whether  it  Avould  be  expedient  for  the  Athenians  to  execute  them.  So 
Canning,  in  a  speech  in  the  House  of  Commons  in  reply  to  Mr.  Per- 
ceval, says,  "  The  question  is  not,  as  assumed  by  my  opponent,  whether 
we  shall  continue  the  war  in  the  Peninsula,  but  whether  it  is  essential 
to  our  success  in  the  war  that  our  present  system  of  currency  remain 
unchanged."  Thus  it  is  not  unusual,  after  a  protracted  debate,  for  the 
cooler  thinkers  to  preface  their  remarks  with  reminding  the  audience 
of  the  real  nature  of  the  point  on  which  issue  is  joined ;  and  the  longer 
and  more  heated  the  discussion,  the  greater  the  need  for  these  moni- 
tory exordiums.  For,  especially  when  the  field  of  debate  is  large,  the 

19  TImcydides,  bk.  iii,  year  5. 


278  OF    FALLACIES. 

combatants  often  join  issue  on  the  wrong  points,  or  do  not  join  issue 
at  all.  One  goes  to  the  east,  another  to  the  west ;  one  loses  the  prop- 
osition in  question,  and  wanders  amidst  a  crowd  of  irrelevant  details; 
another  mistakes  contraries  for  contradictories,  or  universals  for  par- 
ticulars ;  and,  after  some  hours  of  storm,  they  know  not  what  they 
hav£  been  discussing.  One  has  made  out  a  case  which  his  adversary 
admits,  the  more  readily  as  it  has  not  the  least  bearing  on  the  ques- 
tion ;  another,  having  overthrown  a  similar  collateral  proposition, 
makes  his  pretended  triumph  resound  over  the  field;  yet  another, 
having  been  rather  shattered  by  reasons,  appeals  to  the  prejudices  of 
his  auditory,  and,  overwhelming  his  more  rational  antagonist  with 
ridicule  and  abuse,  comes  off  the  apparent  and  acknowledged  victor 
in  the  contest.1* 

And  this  reminds  us  that  the  ignoratio  or  mutatio  often  takes  the 
form  of  personalities.  We  dispute  with  warmth,  and  without  under- 
standing one  another.  Passion  or  bad  faith  leads  us  to  attribute  to 
our  adversary  what  is  far  from  his  meaning,  in  order  to  carry  on  the 
contest  to  greater  advantage.  It  is  a  sign  both  of  weakness  and  de- 
pravity that  in  almost  every  dispute  the  debaters  ignore  the  question, 
and  aim  their  tongues  or  their  pens  at  their  antagonists.  In  all  the 
controversies  that  have  shaken  the  opinions  of  mankind,  this  tendency 
is  visible.  In  politics,  the  epithets  radical  and  rebel,  tyrants  and  trai- 
tors, have  for  ages  been  watchwords  and  weapons.  In  philosophy, 
the  terms  materialist,  sensualist,  idealist,  transcendentalist,  are,  in  dif- 
ferent mouths,  terms  of  admiration  or  contempt.  In  religion,  the 
names  Quaker  and  Methodist  are  memorials  of  scorn  in  the  past ;  and 
"heretics,"  "bigots,"  "fanatics"  are  plentiful  in  the  present.  We 
rush  at  the  throat  of  our  antagonist,  and  the  world,  delighting  in  a 
display  of  pugnacity,  crowns  the  fiercer  and  more  vituperative  com- 
batant. But  argument,  not  abuse ;  reason,  not  ridicule,  is  the  touch- 
stone of  truth.  What  if  Luther  did  and  wrote  many  absurd  things? 
This  does  not  prove  the  authority  of  the  Roman  Church.  What  if 
Calvin  did  burn  Servetus?  This  does  not  prove  Calvinism  to  be 
fanaticism.  The  success  of  Pascal's  vituperative  Provincial  Letters 
is  very  little  to  the  honor  of  their  author,  for  it  indicates  at  once  the 
weakness  of  those  he  attacked  and  of  those  whom  he  thus  aroused  to 
join  in  his  hostility.  The  satirists  of  all  ages  have  done  as  little  for 
truth  as  Juvenal  did  for  the  morality  of  Rome. 

14  Sydney  Smith's  well-known  Jew  cTesprit,  "The  Noodle's  Oration,"  furnishes 
some  amusing  examples  of  the  Irrelevant  Conclusion. 


SOPHISMS    IN    MATTER.    \  ,.£>.,.  279 


Again,  the  ignoratio  is  often  a  mere  dodge.  Instead  of  even  a  pre- 
tended confutation,  something  is  offered  which  answers  practically. 
A  sophist  defending  one  who  has  been  guilty  of  peculation,  which  he 
wishes  to  extenuate,  but  cannot  disprove,  may  succeed  by  making  the 
jury  laugh.  On  the  other  hand,  the  prosecutor,  if  extenuating  circum- 
stances have  been  proved,  may  dodge  the  question,  and  practically  at- 
tain his  end  by  exciting  the  disgust  of  the  jury,  saying,  "  Well,  but, 
after  all,  the  fellow  is  a  thief,  and  that  is  the  end  of  the  matter," 
which,  however,  not  being  denied,  is  not  the  question.  Here  the  fal- 
lacy appears  as  an  abuse  of  the  argumentum  ad  populum.  Emotion 
succeeds  where  reason  fails.  Likewise  the  argumentum  ad  kominem, 
an  appeal  to  personal  opinion,  and  the  argumentum  ad  verecundiam, 
an  appeal  to  respected  authority,  and  other  modes  of  arguing,  in  them- 
selves legitimate,  may  be  abused  to  establish  irrelevant  conclusions. 

Another  form  is  to  prove  or  disprove  a  part  of  what  is  required, 
and  to  dwell  on  that,  suppressing  the  rest.  This  is  the  dodge  of  prej- 
udiced book-reviewers.  Its  frequent  success  shows  the  danger  of  bring- 
ing in  bad  arguments  to  support  a  good  cause.  Many  a  guilty  prisoner 
has  been  acquitted,  because  some  one  witness  against  him  has  been 
caught  lying.  Vulnerable  points  should  not  be  exposed.  Achilles 
would  have  been  alive  now  had  he  never  shown  a  clean  pair  of  heels. 

Yet  another  form  consists  in  showing  that  there  are  objections  to  the 
proposition,  and  thence  inferring  that  it  should  be  rejected,  when  it 
ought  to  be  proved  that  the  objections  against  receiving  it  are  weightier 
than  the  reasons  for  it.  Objections  can  be  raised  against  any  reform, 
and  even  against  Christianity  itself.  "  There  are  objections,"  said  Dr. 
Johnson,  "  against  a  plenum,  and  also  against  a  vacuum ;  but  one  or 
the  other  must  be  true."  To  suspend  judgment  until  all  objections 
are  removed  is  practically  to  decide  in  favor  of  the  existing  state  of 
things.  "  Not  to  resolve  is  to  resolve,"  says  Bacon. 

Let  us  remark,  in  closing,  that  the  fallacy  of  irrelevant  conclusion  is 
greatly  aided  by  the  adroit  practice  of  suppressing  the  statement  of  the 
conclusion,  and  leaving  it  to  be  supplied  by  the  hearer,  who  then 
is  less  likely  to  perceive  whether  it  be  the  proper  one  or  not.16 


15  See  Whately's  Logic,  pp.  240-249.  De  Morgan  classifies  under  I.  elenchi  any 
attempt  to  transfer  the  onus  probandl  to  the  .wrong,  side.  The  burden  of  proof  al- 
ways lies  properly  on  the  party  making  an  assertion,  whether  positive  or  negative. 
If  he  shifts  this  burden  onto  his  disputant,  demanding  a  disproof  of  his  bare  as- 
sertion, there  is  a  mulatto  which  may  fairly  be  referred  to  this  sophism. 


280  OF    FALLACIES. 

§  4.  The  fourth  class,  Fallacia  consequents  (TO  napa  TO 
gives  rise  to  fallacy,  says  Aristotle,  "  because  the  consecution  of  ante- 
cedent and  consequent  seems  reciprocal.  If  B  follows  from  A,  we 
imagine  that  A  must  follow  from  B.  Because  whatever  is  generated 
has  a  beginning,  it  need  not  be  that  whatever  has  a  beginning  is  gen- 
erated. Because  every  man  in  a  fever  is  hot,  it  does  not  follow  that 
every  man  who  is  hot  is  in  a  fever."  16  These  examples,  at  first  glance, 
seem  to  be  merely  the  fallacy  of  converting  simply  a  universal  affirma- 
tive. This  cannot  be  Aristotle's  meaning.  Let  us  examine  further. 
Subsequently  he  says,17  "  In  another  mode  of  this  falsely  inferred  con- 
sequence, the  relation  of  the  contradictories  of  the  antecedent  and 
consequent  is  supposed  to  correspond  directly  to  the  relation  of  the 
antecedent  and  consequent.  If  B  follows  from  A,  it  is  falsely  as- 
sumed that  non-B  follows  from  non-A.  So  in  Melissus's  argument,  if 
the  generated  is  limited,  the  ungenerated  is  unlimited;  so  that  if  the 
heavens  are  uncreated,  they  are  boundless."  This  makes  it  sufficiently 
plain  that  Aristotle's  F.  consequentis  is  to  infer  the  truth  of  the  ante- 
cedent from  the  truth  of  a  consequent,  and  to  infer  the  falsity  of  the 
consequent  from  the  falsity  of  an  antecedent.  When  it  is  admitted, 
If  A  is,  then  B  is,  we  cannot  say,  But  B  is,  and  therefore  A  is ;  nor 
can  we  say,  But  A  is  not,  and  therefore  B  is  not.18 

16  De  Soph.  ch.  v.  17  Id.  ch.  xxviii. 

18  De  Morgan  states  the  P.  consequentis  to  be  simply  the  affirmation  of  a  conclu- 
sion which  does  not  logically  follow  from  the  premises,  a  mere  non  sequitur. 
His  example  is : 

Episcopacy  is  of  Scripture  origin ; 

The  Church  of  England  is  the  only  episcopal  church  in  England ; 
.'.  The  church  established  is  the  church  that  should  be  supported. 

The  maintenance  of  the  logic  of  this,  he  says,  as  "  consecutive  and  without  flaw," 
was  recently  imputed  by  an  English  newspaper  to  the  clergy  ;  which,  he  adds,  Avas 
hard  on  the  clergy.  Truly,  for,  being  sexipedalian,  it  is  merely  a  logical  insect. 
But  De  Morgan's  definition  will  apply  equally  well  to  any  and  every  fallacy ;  is,  in 
fact,  a  proper  definition  of  logical  fallacy  in  general.  This,  then,  could  not  have 
been  the  meaning  of  Aristotle,  nor  of  the  schoolmen,  his  studiously  passive  fol- 
lowers, who  surely  meant  to  be  specific.  Neither  De  Morgan  nor  Hamilton,  who 
omits  all  mention  of  this  sophism  in  his  Lecture  xxiii,  seems  to  have  looked  into 
the  treatise  De  Soplmtid  Eknclti.  The  former  apparently  draws  from  Aldrich, 
who  misses'  the  point  entirely.  Nor  is  Aldrich  corrected  by  Mansel  in  his  notes. 
Bain  views  the  examples  as  merely  erroneous  conversions  (p.  675).  No  recent 
writer  seems  properly  to  apprehend  the  scope  of  this  species ;  and  the  false  rea- 
soning duly  included  by  it,  if  treated  at  all,  is  treated  entirely  out  of  place. 


SOPHISMS    IN    MATTER.  281 

This  inconsequence  has  already  been  noticed  under  Paralogisms, 
where  the  formal  fault  is  pointed  out.  But  the  fallacy  is  often  con- 
cealed by  the  matter,  and  beclouded  by  feeling.  People  continually 
think  and  express  themselves  as  if  they  believed  that  the  premises 
cannot  be  false  if  the  conclusion  is  true.  The  truth,  or  supposed  truth, 
of  the  inferences  which  follow  from  a  doctrine  often  enables  it  to 
find  acceptance  in  spite  of  its  gross  absurdity.  How  many  philo- 
sophical systems  which  had  scarcely  any  intrinsic  recommendation 
have  been  received  by  thoughtful  men  because  they  were  supposed  to 
lend  additional  support  to  religion,  morality,  some  favorite  view  in 
politics,  or  some  other  cherished  persuasion  ;  not  merely  because  their 
wishes  were  thereby  enlisted  on  its  side,  but  because  its  leading  to 
what  they  deemed  sound  conclusions  appeared  to  them  a  strong  pre- 
sumption in  favor  of  its  truth  ! 19 

And,  on  the  other  hand,  a  good  cause  supported  by  false  premises 
or  a  bad  argument  falls  into  disrepute.  A  notable  instance  is  the 
cause  of  Temperance.  Its  warm  and  extreme  advocates  adduce  in  its 
favor  an  appalling  amount  of  misstatement  and  of  distorted  and  dis- 
proportioned  facts ;  and,  again,  from  unquestionable  facts  they  some- 
times reach  their  conclusions  by  a  startling  logic  unknown  to  Aris- 
totle and  his  slow-gaited  followers.  Now  the  argument  for  this  good 
cause  is  very  simple  and  impregnable ;  but,  unfortunately,  it  does  not 
furnish  material  enough  for  the  popular  oratory  of  the  day,  which, 
therefore,  soars  untethered  by  fact  or  logic.  The  revulsions  the  cause 
has  suffered  ought  to  teach  its  advocates  that  a  bad  argument  is  worse 
than  no  argument.  For  when  people  discover  the  fallacy,  they  in- 
stantly commit  the  counter-fallacy,  and  conclude  that  because  a 
premise  is  false,  or  the  argument  illogical,  therefore  the  conclusion 
is  false ;  and  so  the  last  state  of  that  cause  is  worse  than  the  first. 
Whoever  would  think  truly  should  hold  steadily  to  the  principle  that 
in  such  case  the  conclusion  is  not  disproved,  but  merely  unproven. 
An  indictment  fails,  and  the  prisoner  is  declared  "Not  guilty," 
which,  I  take  it,  is  an  abbreviation  for  "  not  proved  guilty."  But  the 
people  conclude  he  has  been  "  found  innocent."  True,  he  is  to  be 
presumed  innocent  until  found  guilty ;  but  presumption  is  not  proof. 
The  more  deliberate  and  skilful  the  criminal,  the  more  likely  is  he 
to  win  this  verdict.  The  vast  remove  between  unproved  guilt  and 
innocence  ought  to  be  clearly  marked. 

19  Mill's  Logic,  p.  560. 


282  OF    FALLACIES. 

§  5.  The  fifth  class  is  Petitio  principii  (TO  napa.  TO  kv  upxy  XajLr/3d- 
vtiv  1}  aiT£~iffdat).  Says  Aristotle,  "Petition  (curate)  is  an  assump- 
tion opposed  to  the  belief  of  the  hearer ;  or,  still  wider,  a  proposition 
requiring  proof  assumed  without  proof."  a  Elsewhere  he  says  that 
the  Petitio  qucesiti,  as  this  sophism  may  more  correctly  be  called,81  or 
begging  the  question,  "  appears  to  occur  in  five  ways.  The  first  and 
most  manifest  way  is  when  the  very  thing  that  should  be  proved  is 
assumed.  This  cannot  easily  pass  undetected  when  the  terms  are  the 
same ;  but  when  synonyms  are  used,  or  a  name  and  its  definition  or  a 
circumlocution,  it  may  escape  detection.  A  second  way  is  when  a 
particular  is  to  be  proved,  and  the  universal  is  assumed ;  as,  for  in- 
stance, if  we  have  to  prove  that  contraries  are  objects  of  a  single  sci- 
ence, and  assume  that  opposites,  their  genus,  are  objects  of  a  single 
science.  It  appears  that  what  should  be  proved  alone  is  assumed  in 
company  with  other  propositions.  A  third  way  is  when  a  universal 
is  to  be  proved,  and  the  particular  is  assumed ;  as  when  what  ought 
to  be  proved  of  all  contraries  is  assumed  of  some.  Here  it  appears 
that  what  is  to  be  proved  in  company  with  other  propositions  is  as- 
sumed alone.  A  fourth  way  is  when  we  divide^  the  question  to  be 
proved,  and  assume  it  in  detail ;  as  when  we  have  to  prove  that  medi- 
cine is  the  science  of  health  and  disease,  and  successively  assume  it  to 
be  the  science  of  each.  A  fifth  way  is  when  two  facts  are  reciprocally 
involved,  and  we  assume  the  one  to  prove  the  other ;  as  when  we 

20  Anal.  Post,  i,  10. 

21  Petitio  principii  is  rather  a  blundering  translation  of  the  Avistotelic  phrase, 
though  of  universal  acceptance.    In  his  Metaphysics,  iv,  i,  3,  Aristotle  defines  "  prin- 
ciple," in  general,  as  "  that  from  which  anything  exists,  is  produced,  or  is  known." 
It  is  always  and  properly  used  for  that  on  which  something  else  depends ;  and 
thus  both  for  an  original  law  and  for  an  original  dement.     Cf.  Hamilton's  Reid,  p. 
761.     The  fallacy  before  us  is  the  assumption,  not  of  the  principle  properly  so 
called,  but,  in  some  form  or  other,  of  the  qiwstion  originally  proposed  for  proof. 
Pacius,  in  his  Cvtnmentarius  in  Organon  (in  Anal.  Prior,  ii,  16),  says,  "Non  est 
petitio  rrJQ  «px$£'  ^  es^  Prineipi^  vel  *"  ry  "PXVi  ^  €S*i  *n  principle ;  sed  TOV  iv 
dpxy  TrpoKtijikvov,  id  est,  ejus  problematis,  quod  initio  fuit  proposituni  et  in  disqui- 
sitionem  vocatum."     See  also  Hamilton's  Logic,  p.  369 ;  and  Hansel's  Aldridi, 
Appendix^  note  E. 

We  have  rather  a  startling  etymology  of  the  phrase  furnished  us  by  Du  Marsias, 
Logique,  p.  81,  which  is  worth  preserving  for  its  own  sake:  "Co  mot  s'appelle 
petition  de  principe,  du  mot  grcc  Trcro/jcu,  qui  signifie  voler  vcrs  quelque  chose,  et  du 
mot  latin  principium,  qui  veut  dire  commencement;  ainsi  faire  line  petition  de  prin- 
cipe, c'est  recourir  en  d'autres  termes  a  la  meme  chose  que  ce  qui  a  d'abord  etc 
mis  en  question." 


SOPHISMS    IN    MATTER.  283 

assume  that  the  side  of  a  square  is  incommensurate  with  the  diagonal, 
when  we  have  to  prove  that  the  diagonal  is  incommensurate  with  the 
side."  "  The  first  two  of  these  five  modes,  they  being  the  most  im- 
portant, we  will  now  proceed  to  illustrate  at  some  length. 

The  first  mode  of  this  sophism  occurs  when  a  premise  is  either  the 
same  in  sense  as  the  conclusion,  or  else  actually  proved  from  it.  This 
indicates  two  varieties,  named  the  Hysteron  protcron,  and  the  Circle. 

The  former  (vcrrepov  TrpoTepov),  wherein  the  conclusion  and  a  prem- 
ise are  in  sense  the  same,  does  not  extend  beyond  a  single  proposition 
or  syllogism ;  e.  g.,  "  The  doctrine  is  heretical,  for  it  has  wrought  a 
schism  in  the  church."  A  proposition  which  is  thus  a  corollary  from 
itself  would  not,  by  any  person  in  his  senses,  be  considered  as  therein 
proved,  were  it  not  expressed  in  language  which  makes  it  seem  to  be 
two.  It  is  not  uncommon  that  a  proposition  expressed  in  abstract 
terms  is  offered  as  proof  of  the  same  proposition  expressed  in  con- 
crete terms.  Pretended  proof  and  pretended  explanation  both  take 
this  form ;  e.  g.,  The  loadstone  attracts  iron  because  of  its  magnetic 
power.  This  is  burlesqued  by  Molierc  in  the  speech  of  Bachelierus : 23 

"Mihi  a  docto  doctore 
Deraandatur  causam  ct  rationem  quare 

Opium  facit  dorraire. 
A  quoi  respondeo : 
Quia  est  in  eo 
Virtus  dormitiva, 
Cujus  est  natura 

Sensus  assoupire." 

The  English  language,  being  compounded  of  several  languages,  is  pe- 
culiarly well  fitted  for  this  form  of  petitio  principii.  We  make  an 
affirmation  in  words  of  Saxon  origin,  and  offer  as  a  reason  or  explana- 
tion the  same  in  words  of  Norman  origin,  and  vice  versa;  e.  g.,  The 
bill  before  the  House  is  well  calculated  to  elevate  the  character  of 
education  in  the  country,  for  the  general  standard  of  instruction 
in  all  the  schools  will  be  raised  by  it.  These  are  "  ladies'  reasons." 
It  is  so.  Why  ?  Because  it  is  so.  The  propositions  are  merely  equi- 
pollent, and  should  be  distinguished  from  immediate  inferences. 

23  Topica,  viii,  13.  Aristotle  then  proceeds  to  distinguish  five  modes  also  of 
Petitio  contrariorum.  In  petitio  principii  the  wrong  procedure  has  reference  to 
and  affects  the  conclusion ;  in  petitio  contrariorum  it  affects  only  the  contrary 
propositions  themselves  and  the  relation  subsisting  between  them.  For  a  para- 
phrase of  these  five  modes,  see  Grote's  Aristotle,  vol.  ii,  p.  62. 

33  Le  Halade  Imaginaire :  Troisieme  Intermede. 


284  OF    FALLACIES. 

This  fallacy  does  not,  however,  require  a  proposition,  but  occurs  in 
what  Bentham  calls  "  question-begging  appellatives ;"  meaning,  names 
which  beg  the  question  under  guise  of  stating  it.  The  names  of  po- 
litical parties,  as  Democratic,  Republican,  Liberal,  Conservative,  arc 
much  used  in  this  way ;  e.  g.,  "  Those  who  favor  the  preservation  of 
the  fundamental  principles  of  our  government  should  of  course  act 
with  the  Conservative  party."  These  are  potent  when  laudatory,  but 
even  more  so  when  vituperative ;  as,  Radicals,  Rebels,  and  most  po- 
litical catchwords.  The  word  "innovation"  having  acquired  a  bad 
sense,  the  admission,  which  is  unavoidable,  that  a  new  measure  is  an 
innovation  is  always  construed  to  its  disadvantage. 

Galileo  has  accused  Aristotle  himself  of  being  guilty  of  petitio 
principii  in  the  following  argument : 

The  nature  of  heavy  things  is  to  tend  to  the  centre  of  the  universe,  and  of  light 

things  to  fly  from  it ; 
Now  experience  proves  that  heavy  things  tend  towards  the  centre  of  the  earth, 

and  that  light  things  fly  from  it ; 
.'.  The  centre  of  the  earth  is  the  centre  of  the  universe. 

How  could  Aristotle  say  in  the  major  that  heavy  things  tend  to  the 
centre  of  the  universe,  except  by  assuming  that  the  two  centres  are 
identical,  which  is  what  he  undertakes  to  prove.84 

Plato,  in  the  Sophistes,  attempts  to  prove  that  things  may  exist 
which  are  incorporeal,  by  the  argument  that  wisdom  and  justice  arc 
incorporeal,  and  wisdom  and  justice  must  be  something.  Here,  if  by 
"  something"  be  meant,  as  Plato  did  in  fact  mean,  a  thing  capable  of 
existing  in  and  by  itself,  and  not  as  the  quality  of  some  other  thing, 
he  begs  the  question ;  if  he  means  anything  else,  the  conclusion  does 
not  follow.  This  fallacy  might  also  be  classed  as  ambiguous  middle ; 
"something"  in  the  one  premise  meaning  some  substance,  in  the 
other,  some  object  of  thought,  whether  substance  or  attribute. 

It  was  once  an  argument  for  the  infinite  divisibility  of  matter,  that 
every  portion  of  matter,  however  small,  must  have  an  upper  and  an 
under  surface.  Those  using  this  argument  did  not  see  that  it  assumed 
the  very  point  in  dispute,  the  impossibility  of  arriving  at  a  minimum 
of  thickness ;  for  if  there  be  a  minimum,  its  upper  and  under  surface 
will  of  course  be  one ;  it  will  be  a  surface,  and  nothing  more.  The 
argument  is  very  plausible  because  the  premise  seems  more  obvious 
than  the  conclusion,  though  really  identical  with  it.25 

84  Arnauld,  p.  249.  ™  Mill's  Logic,  p.  574. 


SOPHISMS    IN    MATTER.  285 

The  formal  fault  of  Hysteron  proteron  is  that  it  is  a  pretended 
syllogism  of  two  terms  only, — a  logical  biped.  This  is  disguised  by 
the  usual  enthymemic  mode  of  stating  but  two  of  the  propositions, 
and  by  giving  them  in  different  words.  The  forms  are  these, — 

A  is  B  ;  A  is  B ; 

A  is  B ;  A  is  A ; 

.'.  A  is  B.  .'.  A  is  B. 

There  is  no  step  forward  here;  it  is  merely  "marking  time." 

We  can  now  understand  why  Aristotle,  in  the  passage  quoted,  dis- 
tinctly condemns  the  premising  of  definitions  as  this  mode  of  petitio 
principii.  Let  us  consider  the  following: 

Every  rectilinear  figure  of  three  sides  has  its  angles  equal  to  two  right  angles ; 
Every  triangle  is  a  rectilinear  figure  of  three  sides ; 
.'.  Every  triangle  has  its  angles  equal  to  two  right  angles. 

Here  the  minor  premise  is  a  definition.  Now  the  subject  and  predi- 
cate of  a  defining  proposition  are  identical  in  thought,  the  latter 
merely  being  explicit.  The  point  to  be  proved,  in  the  above  example, 
is  that  the  three-sided  figure  has  its  angles  equal  to  two  right  angles, 
whether  it  be  called  a  triangle  or  not.  This  is  assumed  in  the  major 
premise,  and  reiterated  in  the  conclusion.  The  example  is  obviously 
in  the  second  of  the  two  preceding  forms.28  Whenever  cither  ex- 
treme of  an  apparent  syllogism  is  identical  in  thought  with  the  mid- 
dle term,  there  are  of  course  but  two  terms,  however  much  the  phra- 
seology may  change.  Such  a  pseudo-syllogism  involves  mere  itera- 
tion, and  no  progress  of  thought;  the  conclusion  has  already  been 
stated  in  a  premise,  and  nothing  is  proved.  It  is  merely  the  replace- 
ment of  a  term  by  its  definition,  or  the  reverse;  as  in  the  following: 
"  The  effect  of  the  proposed  measure  will  be  to  depress  wages  and  to 
oppress  all  needy  persons,  since  lower  rates  of  payment  for  labor  will 
be  caused  by  it,  and  a  cruel, unjust  burden  laid  upon  the  poor." a 

The  use  of  a  proposition  to  prove  that  on  which  it  is  itself  depend- 
ent for  proof  by  no  means  implies  the  degree  of  mental  imbecility 

36  See  also  the  "  Demonstratio  potissima  "  in  Part  4th,  iii,  §  1. 

27  I  am  strongly  inclined  to  the  opinion  that  this  view  might  be  extended  to  the 
analytic  and  synthetic  judgments  of  Kant  (see  Part  3d,  i,  §  12).  Perhaps  it  would 
be  correct  to  say  that  any  syllogism  having  either  premise  a  mere  anaI}Ttical  judg- 
ment, unfolding  what  is  contained  in  a  name,  is  petilio  principii,  and  actually 
proves  nothing ;  and  that  only  those  whose  premises  are  synthetical  judgments,  a 
conjunction  of  distinct  facts,  amount  to  actual  proof.  If  so,  this  would  modify  the 
defence  of  the  syllogism  (Part  4th,  ii,  §  8)  and  facilitate  it. 


286  OF    FALLACIES. 

which  might  be  supposed.  The  difficulty  of  comprehending  how  this 
sophism  can  possibly  be  committed  disappears  when  we  reflect  that 
all  persons,  even  the  instructed,  hold  a  great  number  of  opinions  with- 
out exactly  recollecting  how  they  came  by  them.  Hence  they  may 
easily  be  betrayed  into  deducing  them  alternately  from  one  another. 
A  person  may  at  one  time  insist  on  the  divine  origin  of  the  Scriptures 
because  they  contain  certain  sublime  doctrines  which  could  not  be 
discovered  by  the  natural  sagacity  of  the  writers;  at  another  time  he 
may  insist  that  these  doctrines  are  true  because  found  in  the  Script- 
ures, which,  being  of  divine  origin,  are  to  be  wholly  accepted.  So 
Plato,  says  Hamilton,*8  in  his  Phcedo,  demonstrates  the  immortality  of 
the  soul  from  its  simplicity ;  and,  in  the  Republic,  demonstrates  its 
simplicity  from  its  immortality. 

When  a  premise  and  conclusion  which  are  actually  the  same  are 
thus  somewhat  remote  from  each  other,  this  variety  of  the  first  mode 
of  petitio  principii  is  called  "Reasoning  in  a  Circle,"  Orbis  vel  circulus 
in  demonstrando,  vel  diallelus  (Si  aXX?'/Xwr).  The  form  may  be  rep- 
resented as  a  pro-  and  epi-syllogism,  thus : 

A  is  B ;  C  is  B ; 

C  is  A ;  then—  A  is  C ; 

/.  C  is  B.  /.  A  is  B. 

Of  course  any  number  of  syllogisms  may  intervene,  and  the  greater 
the  number  of  intermediate  steps,  the  more  likely  is  the  sophism  to 
escape  detection.  A  man  walking  around  a  hill  is  fully  conscious 
of  his  circular  movement ;  not  so  when  he  walks  along  a  meridian  line. 
Hence,  to  expose  this  fallacy,  we  have  only  to  narrow  the  circuit  by 
casting  out  intermediate  steps,  and  exhibit  the  proposition,  when  it 
comes  round  again,  in  the  same  words. 

The  following  example  of  reasoning  in  a  circle  is  from  "Whately:29 

Every  particle  of  matter  gravitates  equally. 

Why  ?     What  reason  have  you  for  that? 

Because  those  bodies  which  contain  more  particles  ever  gravitate  more  strongly ; 

that  is,  are  heavier. 

But  those  which  are  heavier  are  not  always  more  bulky. 
No,  but  still  they  contain  more  particles,  though  more  closely  condensed. 
How  do  you  know  that  ? 
Because  they  are  heavier. 
How  does  that  prove  it  ? 
Because,  all  particles  of  matter  gravitating  equally,  that  mass  which  is  specifically 

the  heavier  must  needs  have  the  more  of  them  in  the  same  space. 

46  Logic,  p.  372.  89  Logic,  p.  221. 


SOPHISMS    IN    MATTER.  287 

On  this  Mill  remarks  that  such  a  process,  wherein  there  is  an  actual 
attempt  to  prove  two  propositions  reciprocally  from  one  another,  is 
seldom  resorted  to,  at  least  in  express  terms,  by  any  person  in  his  own 
speculations,  but  is  more  likely  to  be  committed  by  one  who,  being 
hard  pressed  by  an  adversary,  is  forced  into  giving  reasons  for  an 
opinion  of  which,  when  he  began  to  argue,  he  had  not  sufficiently 
considered  the  grounds.  Hence  another  way  to  expose  a  Diallelon : 
challenge  the  reasoner  to  prove  his  premise,  which  if  he  undertakes  to 
do,  his  whirl  is  evolved.30 

A  notable  example  of  reasoning  in  a  circle  is  the  argument  of  Ed- 
wards and  other  metaphysicians  for  a  necessitated  will.  The  will, 
they  affirm,  must  be  subject  to  the  law  of  necessity,  because  its  deter- 
minations are  always,  as  a  matter  of  fact,  in  accordance  with  the 
strongest  motive,  the  greatest  apparent  good.  The  strongest  motive 
determines  the  choice,  hence  the  will  is  necessitated.  But  what  do 
you  mean  by  the  strongest  motive  ?  It  is,  of  course,  the  motive  that 
prevails.  We  know  that  it  is  the  strongest  because  it  does  prevail. 
If  it  were  not  the  strongest,  the  will  would  not  have  followed  it ;  and 
being  the  strongest,  the  will  must  follow  it.  Then  that  is  to  say,  the 
will  must  follow  the  strongest  motive,  because  the  strongest  motive  is 
the  one  the  will  must  follow. 

The  second  mode  of  petitio  principii  is  that  in  Avhich  a  universal  is 
assumed  to  prove  a  particular.  For  example :  "  Is  William,  King  of 
Germany,  in  any  respect  tyrannical?  Of  course  he  is;  for  all  men 
possessing  power  are  more  or  less  tyrannical." 

It  is  remarkable  that  this  does  not  differ  in  form  from  the  legiti- 
mate syllogism.  It  seems  to  give  new  ground  for  the  charge,  already 
discussed,81  that  the  Aristotelic  syllogism  is  essentially  peiitio  primipii. 
But  observe  that  the  fault  here  indicated  is  not  a  formal  fault ;  it  does 
not  lie  within  the  syllogism  itself,  but  precedes  it.  It  lies  in  the  as- 
sumption of  a  principle  by  the  reasoner,  from  which  the  conclusion 
truly  follows,  but  which  stands  in  need  of  proof  as  much  or  even  more 
than  the  conclusion  itself,  and  therefore  cannot  establish  it,  the  whole 

so  Logic,  p.  571.  That  every  particle  of  matter  gravitates  equally  will  not  be 
granted  by  those  who  accept  the  atomic  theory,  according  to  which  the  particles 
have  different  specific  combining  weights.  It  is  true,  however,  that  these  particles, 
though  they  may  be  real  minima  for  the  purposes  of  chemical  combination,  may 
not  be  the  ultimate  particles  of  the  substance ;  and  this  doubt  renders  the  hypoth- 
esis of  equal  weights  admissible  as  an  hypothesis. 

81  Part  4th,  ii,  §  8. 


288  OF    FALLACIES. 

question  being  still  afloat.  This,  then,  is  not  at  all  a  formal  fallacy. 
Its  fault  lies  solely  in  taking  that  for  granted  which  is  not  granted. 
It  would  be  petitio  prindpii  to  prove  to  a  Mohammedan  the  divinity 
of  Christ  from  texts  in  the  New  Testament,  for  he  does  not  admit  the 
authority  of  the  Bible ;  but  it  would  be  a  valid  argumentum  ad  homi- 
nem  to  prove  to  him  from  the  Koran  the  prophetic  mission  of  Jesus, 
for  the  authority  of  the  Koran  he  acknowledges. 

The  phrase  petitio  principii,  the  unwarranted  assumption  of  a  princi- 
ple, or  the  begging  the  question,  is  properly  and  specifically  applied 
to  designate  this  second  mode  of  the  sophism.  It  is  not,  however,  to 
be  understood  as  if  e'very  probation  in  which  anything  is  presupposed 
and  not  proved  were  at  once  to  be  rejected  as  worthless.  If  so,  it 
would  be  necessary  in  every  case  to  ascend  to  the  ultimate  principles 
of  human  knowledge,  and  these  themselves,  being  incapable  of  proof, 
might  be  rejected  as  unwarranted  assumptions.  Were  this  the  mean- 
ing, there  could  be  no  probation  whatever.33  A  probation  is  guilty  of 
this  sophism  only  when  a  proposition  which  may  be  doubted  on  the 
ground  on  which  the  thesis  itself  is  doubted  is  assumed  as  a  princi- 
ple of  proof,  and  we  thus  attempt  to  prove  the  uncertain  by  the  equally 
uncertain.  Sound  probation  must  depart  from  such  principles  as  are 
cither  immediately  given  as  ultimate,  or  mediately  admit  of  proof 
from  other  sources  than  the  proposition  itself  in  question.33  "  It  is 
allowed,"  says  Aristotle,  "  that  when  assumptions  are  closely  connected 
with  the  issue,  we  may  deny  them,  and  refuse  them  as  premises,  on 
the  plea  that  they  beg  the  question."  34 

Among  the  schoolmen  this  second  mode  of  the  sophism  was  of 
peculiar  interest.  The  philosophy  of  their  time  consisted  largely  of 
certain  general  propositions  (principia)  established  by  authority,  and 
supposed  to  be  ultimately  derived  from  intrinsic  evidence.  Among 
these  tenets  were  the  doctrines  of  Aristotle,  which  were  regarded  with 
a  reverence  due  only  to  inspired  Scriptures.  Stultum  est  dicere  Aris- 
totelem  errare.  Others  were  propositions  which  were  considered  as 


83  "The  main  principles  of  reason  are  in  themselves  apparent.  For  to  make 
nothing  evident  of  itself  to  man's  understanding  were  to  take  a\v;iy  all  possibility 
of  knowing  anything.  And  herein  that  of  Theophrastus  is  true,  '  They  that  seek 
a  reason  of  all  things  do  utterly  overthrow  reason.'  " — Hooker,  Ecd.  Pol.  i,  8,  5. 

33  Hamilton's  Logic,  p.  371.     He  further  observes  that  a  saltus  in  probation  is  a 
special  case  of  petitio  ;  for,  by  an  ellipsis  of  an  intermediate  link,  we  use  a  prop- 
osition which  is  actually  without  its  proof. 

34  DC  Soph.  xvii. 


SOPHISMS    IN    MATTER.  280 

having  been  fully  established  by  demonstrations  as  rigorous  as  those 
of  Euclid.  None  were  ever  questioned;  except,  perhaps,  in  rare  cases, 
when,  consequently,  as  in  the  nominalist  controversy,  society  was 
shaken  to  its  foundations  by  a  moral  earthquake.  These  principia, 
being  universally  admitted,  were  at  the  command  of  every  disputant. 
The  syllogism  in  Barbara  had  properly  a  principium  for  its  sumption, 
and  an  cxemplum  for  its  subsumption.  The  petitio  principii  occurred 
when  any  one,  to  prove  his  case,  made  it  an  example  under  a  princi- 
ple which  was  not  among  those  received,  and  which  was  assumed 
without  offering  to  bring  it  under  their  logical  empire.  Thus,  were 
one  to  argue  from  "  Every  being  void  of  reason  must  perish "  that 
therefore  the  brutes  perish,  it  would  be  denounced  as  petitio  principii, 
this  sumption  not  being  found  among  the  acknowledged  principia. 
Again,  suppose  one  to  argue  that  since  "  Entire  liberty  is  essential  to 
well-being  and  happiness,"  civil  law,  being  an  abridgment  of  liberty, 
is  therefore  detrimental  and  should  be  abolished.  To  this  would  be 
replied,  Of  course,  if  your  major  is  true ;  but  unless  you  offer  pre- 
liminary proof,  you  beg  the  question.  We  may  illustrate  further  by 
the  reply  of  Cardinal  Richelieu  to  an  applicant  for  clemency  who 
thought  to  reason  the  matter,  saying,  "  Mais,  monsieur,  il  faut  vivre." 
Said  his  Grace,  "  Je  n'en  vois  pas  la  necessite."  There  is,  perhaps, 
a  breath  of  inhumanity  in  this,  but  logically  it  means  that  the  postu- 
late was  not  among  the  principles  admitted  by  him  as  Cardinal,  and 
that  one  might  reasonably  beg  his  life,  but  not  the  question. 

The  third  mode  of  petitio  principii  assumes  the  particular  to  prove 
the  universal.  Aristotle  himself  seems  to  be  guilty  of  this  when  he 
maintains  that  slavery  is  in  accord  with  natural  law,  on  the  ground 
that  the  neighboring  barbarians,  being  inferior  in  intellect,  are  the 
born  bondsmen  of  the  Greeks.85 

The  fourth  and  fifth  modes  need  no  special  illustration.  Concern- 
ing the  latter,  however,  we  will  remark  how  easy  it  is  to  frame  prop- 
ositions apparently  different  by  the  use  of  opposed  or  correlative 
terms.  For  example,  "Everywhere  the  light  of  life  and  truth  was 
lacking,  for  darkness  covered  the  land,  and  gross  darkness  the  people." 
Again,  "  Alexander  was  the  son  of  Philip;  therefore  Philip  was  the 
father  of  Alexander."  The  last  example  is  cited  by  Dr.  Reid  as  a  case 
of  "  simple  reasoning"  for  which  Logic  does  not  provide.  Truly  so ; 
but,  on  the  other  hand,  Logic  has  been  careful  to  provide  against  it. 

88  Politica,  i,  2. 
19 


290  OF   FALLACIES. 

§  6.  The  sixth  class  is  Non  causa  pro  causa,  (TO  p)  a'inov  u>c  at- 
TLOV  TiQlvat).  "  We  mistake,"  says  Aristotle,36  "  for  a  cause  what  is 
not  a  cause  [meaning,  a  reason  for  what  is  not  a  reason]  when  an  ir- 
relevant proposition  has  been  foisted  into  an  argument  as  if  it  were 
one  of  the  necessary  premises."  His  example  is  a  reductio  ad  impossi- 
ble to  prove  that  "  Life  and  the  soul  are  not  identical ;"  thus : 

We  assume  that  the  opposite  of  destruction  is  generation ; 

Therefore  the  opposite  of  a  particular  destruction  is  a  particular  generation. 

But  death  is  a  particular  destruction,  and  its  opposite  is  life  ; 

Life,  therefore,  is  generation,  and  to  live  is  to  be  generated. —  This  is  absurd. 

Therefore  life  and  the  soul  are  not  identical. — Q.  E.  D. 

The  absurd  conclusion  may  be  a  proper  sequence,  and  its  absurdity 
justify  the  contradiction  of  a  premise.  But  here  an  unexpressed 
premise,  that  "  Life  and  the  soul  are  identical,"  is  mentally  foisted  into 
the  train,  and  its  contradictory  stated  as  the  Q.  E.  D.  It  is  treated  as 
if  it  were  the  cause  of  the  absurd  conclusion,  which  it  is  not,  and  so 
we  have  the  fallacy  of  false  cause,  or  non  causa  pro  causa.  Aristotle 
afterwards  says 37  that  to  detect  this  fallacy  we  must  examine  whether 
the  suppression  of  this  premise  would  interrupt  the  sequence.  If  it 
does  not,  then  we  know  that  it  is  a  superfluous  proposition  foisted  in 
and  treated  as  the  cause  of  the  absurd  conclusion ;  and  this  is  the  fal- 
lacy in  question.  In  the  Prior  Analytics,  he  says,  "  The  most  obvi- 
ous case  of  the  irrelevance  of  the  thesis  to  the  conclusion  is  when  the 
thesis  is  not  connected  by  any  middle  term  with  the  conclusion,  as 
was  said  in  the  Topica  when  discussing  the  sophism  of  non  causa  pro 
causa.  We  should  exemplify  this  if,  to  disprove  the  commensurate- 
ness  of  the  side  of  the  square  to  the  diagonal,  we  appended  an  argu- 
ment for  Zeno's  theorem  that  there  is  no  such  thing  as  locomotion, 
pretending  thereby  to  establish  a  reductio  ad  absurdum"  s 

It  is  clear  that  Aristotle  intended  to  designate  by  non  causa  pro 
causa  the  pretence  that  the  proposition  we  wish  to  refute  is  the  cause, 
in  a  reductio  ad  impossibile,  of  the  false  conclusion  which  in  fact  flows 
from  other  premises;  that  is,  the  sophism  consists  in  maintaining 
that  the  conclusion  is  false  because  that  particular  premise  is  false. 
It  is  a  case  of  sheer  impertinence.  It  arises  in  dialectic  disputation 
from  the  practice  of  asking  the  opponent  to  grant  certain  premises. 
An  unnecessary  proposition  is  asked  and  granted  among  the  rest, 
and  afterwards  it  is  selected  as  the  false  assumption.39 

88  De  Soph.  v.  "  Id.  ch.  xxix.  S8  Ami.  Prior,  ii,  19. 

89  See  Manselj  in  notes  on  Aldrich,  Appendix,  §  4,  4. 


SOPHISMS    IN    MATTER.  291 

Aristotle  does  not,  however,  limit  the  sophism  of  false  cause  to 
cases  of  reductio  ad  impossibile,  but  includes  under  it  all  cases  wherein 
a  conclusion  is  declared  to  exist  by  virtue  of  a  premise  that  does  not 
necessitate  it.  He  himself  is  not  guiltless  of  this  vice.  For  instance, 
he  insists  that  there  are  three  kinds  of  simple  motion,  because  body 
has  three  dimensions,  but  hardly  makes  it  clear  how  the  one  follows 
from  the  other,  i.  e.,  gives  us  no  middle  term  to  connect  these  prop- 
ositions. He  would  prove  also  that  the  heavens  are  unalterable  and 
incorruptible,  because  they  have  a  circular  motion,  and  there  is  no 
motion  contrary  to  circular  motion.  But  what  has  the  contrariety  of 
motion  to  do  with  the  corruption  or  alteration  of  body  ?  And  is  not 
rectilinear  motion  contrary  to  circular? 

This  sophism  has  been  misunderstood,  or  at  least  misstated,  by  per- 
haps all  recent  writers  on  Logic.  We  have  already  noticed  several 
common  misapprehensions,  deviations  from  the  Aristotelic  sense  more 
or  less  grave.  In  this  case  the  error  is  of  sufficient  importance  to  re- 
quire that  the  common  view  be  set  aside  and  the  original  one  re- 
stored. It  is  needful  to  explain  the  deviation  and  to  justify  this 
statement. 

Let  us  first  note  a  distinction  drawn  by  the  old  logicians.  The 
Causa  essendi  is  that  which  determines  the  existence  of  a  fact.  When 
rain  falls  upon  the  ground,  the  ground  is  wet;  the  rain  is  the  cause 
of  the  ground's  being  wet.  The  cause  of  there  being  an  eclipse  of 
the  sun  is  that  the  moon  interposes  between  it  and  the  earth.  The 
Causa  cognoscendi  is  the  cause  of  our  knowing  a  fact.  It  has  rained, 
therefore  I  know  that  the  ground  is  wet.  Here  the  same  thing  is  the 
cause  both  of  the  existence  of  the  fact  and  of  my  knowing  the  fact. 
But  what  is  effect  in  the  first  sense  may  be  cause  in  the  other.  E.  g., 
The  ground  is  wet,  therefore  I  know  it  has  rained.  There  is  an  eclipse 
of  the  sun,  hence  the  moon  must  be  between  it  and  the  earth.40  The 
causa  cognoscendi,  then,  is  the  logical  ground ;  it  is  the  cause  deter- 
mining, not  the  fact,  but  the  judgment.  This  we  now  commonly  call 
the  reason  for,  or  sign  of,  a  thing,  and  use  the  word  cause  only  in  the 
specific  sense  of  causa  essendi*1 

There  can  be  no  doubt  that  Aristotle,  in  the  title  of  the  sophism 
under  consideration,  intended  exclusively  the  causa  cognoscendi,  or  rea- 

40  In  this  inversion,  reasoning  from  effect  to  cause,  we  should  note  that  we  are 
liable  to  the  fallacy  of  Plurality  of  Causes.     An  effect  may  be  due  to  a  variety  of 
causes,  perhaps  to  a  cause  other  than  any  that  have  been  observed. 

41  The  illative  "because"  is  still  used  generically. 


292  OF    FALLACIES. 

son;  and  that  his  followers,  ancient  and  mediaeval,  so  understood  him, 
and  intended  the  same  limitation.43  In  recent  times,  the  word  cause 
becoming  used  almost  exclusively  for  the  causa  essendi,  logicians  have 
commonly  mistaken  his  meaning  and  wrongly  interpreted  this  sophism. 

They  define  the  fallacy  to  be  the  assumption  without  sufficient 
ground  that  one  thing  is  the  cause  (causa  essendi}  of  another.  Thus, 
that  a  change  in  the  moon  is  the  cause  of  a  change  in  the  weather  ; — 
thirteen  at  table  brings  bad  luck ; — the  dog-star,  Sirius,  causes  the  heat 
that  prevails  during  his  ascension.43  Whitcfield  once  attributed  his 
being  overtaken  by  a  hail-storm  to  his  not  having  preached  at  the  last 
town.  Since  many  a  nation  having  a  heavy  debt  has  prospered,  there- 
fore a  national  debt  is  a  national  blessing.  These  are  clearly  instances 
of  the  fallacy  Post  hoc  ergo  propter  hoc,  or  of  Cum  hoc  ergo  propter 
hoc.4*  This  fallacy  is  merely  a  case  of  bad  generalization  or  bad  in- 
duction, and  therefore,  however  important  it  may  be,  has  no  proper 
place  in  Deductive  Logic.  But  by  our  recent  writers  it  is  declared  to 
be  strictly  the  non  causa  pro  causa,  and  is  introduced  and  exclusively 
discussed  in  this  place  and  under  this  title.  Now  it  is  not  only  an 
entire  deviation  from  the  meaning  of  Aristotle  and  the  scholastics 
thus  to  interpret  the  non  causa  pro  causa,  but  also  a  logical  blunder  to 
include  the  inductive  post  hoc  among  the  deductive  fallacies.  On  the 
other  hand,  however  lightly  Aristotle's  non  causa  pro  causa  may  be 
esteemed,  it  clearly  belongs  to  the  deductive  fallacies ;  its  formal  vice, 
since  it  has  no  middle  term,  being  that  it  is  quatcrnio  terminorum. 

Next  to  the  restriction  of  the  word  cause  in  usus  loquendi,  the 
error  was  probably  due  secondarily  to  the  influence  of  Arnauld  and 
Aldrich,  or,  at  least,  was  thereby  confirmed.  The  former  says,  "  The 
non  causa  pro  causa  is  very  common,  and  we  fall  into  it  through  ig- 
norance of  the  true  causes  of  things.  It  is  in  this  way  that  philoso- 
phers have  attributed  a  thousand  effects  to  nature's  abhorrence  of  a 
vacuum  ;  for  instance,  that  vessels  full  of  water  break  when  it  freezes, 
because  the  water  then  contracts,  and  thus  leaves  a  vacuum,  which  nat- 
ure cannot  endure ;"  and  so  on,  through  a  variety  of  illustrations.45 

42  aiTiov  is  fairly  rendered  "  cause,"  but  has  the  general  sense  of  "  that  which  is 
chargeable  with  a  thing ;"  mostly  the  bad  sense  of  "  something  blamable." 

43  See  Virgil,  ^En.  x,  273.   ' 

4*  Says  Cicero,  "  Causa  ea  est  quae  id  efficit  cujus  est  causa.  Non  sic  causa  in- 
telligi  debet,  ut,  quod  cuique  antecedat,  id  ei  causa  sit,  sed  quod  cuique  efficienter 
antecedat." 

48  Port-Royal  Logic,  pp.  251-56. 


SOPHISMS    IN    MATTER.  293 

Aldrich  designates  it  "  Fallacia  a  non  causa  pro  causa ;  sivc  sit  a  non 
vera  pro  vera ;  sive  a  non  tali  pro  tali :  ut,  Cometa  fulsit ;  ergo  Bel- 
lum  erit.  Nullo  modo  ;  nam  si  fuerit,  aliis  de  causis  futurum  est. 
Haec  fallacia  bene  solvitur  negando  causam  falsam  ;  mclius  adducendo 
germanam." 48  Whately,  under  the  influence  mainly  of  Aldrich,  is 
evidently  at  fault.  He  first  accepts  his  mistaken  view,  and  illustrates 
it.  Then,  dissatisfied,  he  guesses  correctly  the  blunder,  that  logicians 
were  confounding  cause  and  reason ;  and  proposes  to  substitute  the 
title  *•  Fallacy  of  Undue  Assumption,"  remarking  that  the  varieties  of 
this  are  infinite.47  Verily ;  for  this  is  merely  to  reason  from  a  false 
premise,  suppressed  or  disguised  in  any  way.  But  such  is  not  a  logi- 
cal fallacy  at  all,  for  Logic  has  nothing  to  do  with  the  falsity  of  the 
premises.  De  Morgan  treats  the  non  causa  pro  causa  very  gingerly. 
lie  says,  "  It  is  the  mistake  of  imagining  necessary  connection  where 
there  is  none,  in  the  way  of  cause,  considered  in  the  widest  sense  of 
the  word."  4  This  is  wide  enough,  truly,  and  might  include  both  the 
right  and  the  wrong.  But  his  examples  show  that  he  takes  the  wrong 
view  only.  For  instance,  he  quotes  the  statement  that  Saunderson 
had  such  a  profound  knowledge  of  music  that  he  could  distinguish 
the  fifth  part  of  a  note ;  and  then  remarks,  "  The  one  who  made  this 
statement  did  not  know,  first,  that  any  person  who  cannot  distinguish 
less  than  the  fifth  part  of  a  note  to  begin  with,  if  he  exhibit  the  least 
intention  of  learning  any  musical  instrument  in  which  intonation  de- 
pends upon  the  ear,  should  be  promptly  bound  over  to  keep  the 
peace ;  and,  secondly,  that  if  Saunderson  were  not  so  gifted  by  nature, 
knowledge  of  music  would  no  more  have  supplied  the  defect  than 
knowledge  of  optics  would  give  him  sight."  These  remarks  show  that 
he  had  only  the  causa  essendi  in  mind ;  for  he  therein  denies  the  as- 
sumption that  knowledge  of  music  was  the  efficient  cause  of  the  dis- 
crimination. And  so  our  recent  English  logicians  generally.49 


48  Logic,  Appendix,  §  4,  4.  4T  Whately's  Logic,  pp.  223-33. 

48  Formal  Logic,  p.  268. 

49  Bain  makes  the  mistake  (Logic,  p.  626  and  p.  675).      Hamilton,  following 
Krug,  misstates  the  meaning  of  non  causa,  and  treats  the  mistaken  view  as  a  de- 
ductive fallacy.     He  also  wrongly  puts  post  hoc  among  the  deductive  fallacies 
(Logic,  pp.  237-39).     Mill  does  not  use  the  title  non  causa  pro  causa,  and  omits  to 
notice  the  Aristotelic  species.    He  puts  the  post  hoc  in  its  appropriate  place  among 
false  inductions.   (See  Logic,  bk.  v,  ch.  v,  on  "  Fallacies  of  Generalization.")    Minor 
writers,  all  that  I  have  examined,  and  they  are  many,  blunder  along  with  passive 
Bequacity. 


294  OF    FALLACIES. 

§  7.  The  seventh  class  is  Plurium  interrogationum  (TO  ra 
epionifiara  tt>  TTOICIJ'),  the  sophism  of  many  questions.  It  is  the  effort 
to  get  a  single  answer  to  several  questions  asked  in  one.  E.  g.,  Was 
Pisistratus  the  tyrant  and  scourge  of  Athens  ?  As  he  was  the  one,  but 
not  the  other,  either  a  yea  or  a  nay  would  commit  the  respondent  to 
a  false  position.  A  variation  is  to  ask  a  single  question,  indeed,  but  so 
stated  or  compounded  that  a  simple  answer  will  assert  or  deny  some 
other  implied  proposition.  E.  g.,  Did  you  take  anything  when  you 
broke  into  my  house  last  night  ?  Are  you  the  only  rogue  in  your 
family?  Have  you  quit  drinking?60  Have  you  cast  your  horns? 
From  this  last  ancient  example,  the  sophism  is  sometimes  called  the 
Cornutus.  "  Several  questions  put  as  one  should  be  met  at  once  by 
the  decomposition  of  the  compound  question  into  its  elements."5 
Obviously  ;  as  in  the  following  example,"  which  has  long  served  as  the 
standard  illustration :  "  Menedemus,  Alexino  rogante,  Numquid  pa- 
trem  verberare  desiisset?  inquit,  Nee  verberavi,  nee  desii."  So  the 
Royal  Society  savans  at  last  solved  the  waggish  query  of  Charles  II : 
Why  does  not  a  live  fish  add  to  the  weight  of  a  bowl  of  water,  as 
a  dead  one  does?  This  implies  two  questions,  which  for  a  time  the 
puzzled  philosophers  overlooked,  viz.  1st,  An  sit?  2d,  Cur  sit?™ 

All  this  seems  quite  frivolous.  The  occasion  for  noting  the  sophism 
is  to  be  found  in  the  eristic  method  of  dialectic  disputation  among  the 
Greeks,  which  proceeds  usually  by  question  and  answer,  the  answers 
being  conventionally  yea  or  nay," — a  method  familiar  to  readers  of 
Plato's  Dialogues.  The  effort  of  the  Sophist  is  to  entrap  his  unwary 
respondent  into  an  admission  which  can  be  turned  against  him  as 
paradoxical.  The  following  example,  borrowed  from  Fries,55  is  attrib- 
uted, in  its  original  form,  by  Diogenes  Laertius  (vii,  §  196),  to  Eubli- 
des  the  Megarian  as  the  inventor: 

Have  you  lost  ten  counters  ? — No. 

Must  you  not  have  lost  what  you  had  at  the  beginning  of  the  game  and  have  not 

now  ? — Yes. 

Have  you  ten  counters  now  ? — No. 
Then  you  have  lost  ten  counters,  and  have  contradicted  yourself. 

But  he  had  lost  only  two  of  the  ten  counters,  and  still  had  eight. 

60  See  Part  3d,  i,  §  12.  B1  De  Soph.  xxx, 

52  Originally  from  Diogenes  Laertius,  ii,  135. 

63  See  the  hackneyed  story  at  length  in  Hamilton's  Metaphysics,  p.  118. 

M  See  De  Soph,  xvii ;  and  Diog.  Laert.  bk.  ii,  ch.  18,  §  135. 

65  Logik,  §  109.    It  is  cited  also  in  De  Soph.  xxii. 


SOPHISMS    IN    MATTER.  295 

It  is  perhaps  worthy  of  remark  that  lawyers  sometimes  nowadays 
badger  unsophisticated  witnesses  in  this  way.  To  some  compound 
question  they  demand  what  they  call  "  a  categorical  answer,"  by 
which  they  mean  a  simple  yea  or  nay,  when  either  answer  will  en- 
trap the  witness  in  a  self-contradiction  or  in  other  falsity.  To  deny 
the  possession  of  a  whole  is  not  to  deny  the  possession  of  a  part,  as 
in  the  above  example  and  in  the  case  of  the  stolen  ham.  To  admit 
the  existence  of  a  certain  motive  (e.  g.,  one  mercenary)  for  an  action 
still  leaves  the  question  undecided  as  to  the  concurrence  of  perhaps 
many  other  motives,  and  says  nothing  of  their  comparative  strength. 

Every  question  containing  an  ambiguous  term  may  be  viewed  as 
double.  Cicero  is  much  puzzled  to  answer  the  question  whether 
anything  vicious  is  expedient.66  Expedient  may  be  understood  either 
as  conducive  to  temporal  welfare  or  as  conducive  to  ultimate  wel- 
fare. If  the  answer,  in  view  of  the  latter  meaning  be  Nay,  an  op- 
ponent may  confute  with  the  former  meaning,  saying,  "But  theft  is 
certainly  vicious,  yet,  as  it  may  conduce  to  temporal  welfare,  it  is  some- 
times expedient."  Or  if  the  answer,  in  view  of  the  former  meaning, 
be  Yea,  he  may  object,  "  But  no  vice  can  ever  conduce  to  ultimate 
good,  therefore  nothing  vicious  is  ever  expedient." 

The  double  question  may  often  be  construed  as  an  incomplete,  and 
hence  false,  disjunction.  Thus  the  Cornutus  may  be  stated,  "  Either 
you  have  cast  your  horns,  or  you  have  them  still ;  which  ?"  But  there 
is  a  third  horn  omitted,  i.  e.,  "  or  you  have  never  had  horns  at  all." 
In  this  form  it  is  merely  a  case  of  a  false  premise. 

The  thirteen  Aristotelic  sophisms  arc  comprised  in  the  following 
mnemonic  hexameters : 

^Equivocat.  Amphi.  Componit,  Dividit,  Ace.  Fi. 
Acci.  Quid,  Ignorans,  Non  Causa,  Con.  Petit.  Interr. 

The  non  causa  is  displaced  here  from  the  original  order  which  is  the 
one  we  have  followed. 

»c  De  Off.  bk.  iii. 


296  OP   FALLACIES. 


IV.  EXAMPLES. 

§  1.  Logic,  from  the  time  of  Aristotle,  became  among  the  Greeks 
a  profession.  The  acute  and  fun-loving  Athenians  especially  busied 
themselves  to  invent  puzzles  with  which  to  entangle  and  deride  the 
stately  professors;  and  these  worthies  themselves  used  the  same 
means  to  discredit  their  rivals.  Many  of  these  puzzles,  together  with 
similar  inventions  by  the  scholastic  logicians,  have  been  handed  down 
the  centuries  to  us,  discussed  at  every  turn.  As  satisfactory  solutions 
were  rare,  they  received  the  title  of  "  Inexplicabiles  Rationes."  They 
\were  collected,  mostly  from  Diogenes  Laertius,  by  Gassendi,  in  his 
.  Liber  de  Origins  et  Varietate  Logicce,  and  are  analytically  reviewed  by 
Hegel.1  Appearing  generally  to  be  a  mere  play  of  wit  and  acuteness, 
we  marvel  at  the  interest  they  have  excited,  at  their  celebrity,  and  at 
the  importance  attached  to  them  by  some  of  the  most  distinguished 
thinkers  of  antiquity.  They  certainly  have  an  historical  interest ;  and 
as  literature  makes  frequent  references  to  them,  the  student  of  Logic 
cannot  neglect  to  make  their  acquaintance. 

The  disguises  which  sophistry  may  assume  are  innumerable.  It 
seems  to  lurk  most  securely  in  the  conditional  forms,  for  these,  being 
often  very  intricate,  are  confusing.  Perhaps  the  most  complete  dis- 
guise is  the  dilemma,  which,  from  its  great  capacity  for  entangled 
statement,  was  the  favorite  form  of  the  Sophists,  and  hence  is  always 
regarded  with  suspicion  and  distrust.  In  some  cases,  however,  very 
simple  forms  have  proved  very  troublesome.  We  will  select  and  ex- 
amine a  few  of  the  most  noted  of  the  Inexplicables.  They  are  known 
by  specific  names  derived  generally  from  the  matter  to  which  they 
were  originally  applied. 

§  2.  The  Achilles  was  proposed  by  Zeno  the  Eleatic,  to  support 
the  leading  tenet  of  Parmenides,  the  unity  of  all  things,  by  showing 
that  the  identity  of  rest  and  motion  is  a  necessary  result  of  the  con- 
trary opinion.  Probably,  however,  he  was  not  serious  in  this  argu- 
ment, but  intended  it  to  retort  the  ridicule  which  had  been  thrown  on 

1  See  Gesch.  der  Fhilos.,Werkc,  xvi,  p.  119  sq. 


EXAMPLES.  297 

the  doctrine  of  his  master  by  involving  his  opponents  in  the  same 
absurdities  that  they  professed  to  find  in  his  theory.a 

The  sophism  runs  thus :  Suppose  that  Achilles  runs  ten  times  as 
fast  as  a  tortoise  that  is  one  mile  in  advance.  Now,  when  Achilles 
has  run  this  mile,  the  tortoise  has  advanced  yV  of  a  mile  beyond. 
When  his  pursuer  has  run  this  TV,  the  tortoise  has  advanced  T-J-y  of  a 
mile  farther;  and  then  TTJVo  of  a  mile;  and  so  on,  ad  infinitum. 
Hence  Achilles  can  never  overtake  the  tortoise. 

Hamilton  pronounces  this  a  sound  argument,  though  leading  to 
palpable  falsehood.  Whately  says  the  pretended  demonstration  can- 
not possibly  be  exhibited  in  syllogistic  form.3  This  confession,  says 
Hansel,  is  a  surrender  of  the  syllogistic  criterion.  But  nothing  is 
easier.  Thus : 

Any  space  equal  to  ffc-  +  -I~  +  TTrinr  +  -  -  -  is  infinite,  being  the  sum  of 

an  infinite  series ; 

The  space  to  be  passed  over  by  Achilles  is  equal  to  this  sum ; 
.'.  This  space  is  infinite. 

The  whole  mystery  of  this  famous  sophism  lies  in  this:  The  major 
premise  is  false.  The  sum  of  an  infinite  series  may  be,  and  in  this 
case  is,  finite.  The  premise  is  equally  false,  whether  space  is  or  is  not 
divisible  ad  infinitum.  This  is  the  solution  given  by  Descartes.4 
The  solution  attempted  by  Coleridge5  is  refuted  by  Herbart.  Mill 
says 6  the  fallacy  lies  in  the  ambiguity  of  the  word  "  infinite,"  in  the 
tacit  and  false  assumption,  as  Hobbes  hinted,  that  whatever  is  infi- 
nitely divisible  is  infinite.  The  argument  proves  that  to  pass  through 
a  finite  space  requires  a  time  that  is  infinitely  divisible,  but  not  an  in- 
finite time.  This  is  tantamount  to  the  solution  of  Descartes.  Viewed 
as  having  a  false  premise,  it  is  not  a  logical  fallacy.  Viewed  as  in- 
volving an  ambiguous  term,  it  is  a  quaternion. 

Aldricli  says,  "Solvitur  ambulando,  quod  fecit  Diogenes."  This 
reminds  us  that  Dr.  Johnson,  in  like  view,  thought  he  refuted  Berke- 
ley's idealism  by  kicking  a  stone.  Zeno  and  Berkeley  affirm  that 
reason  contradicts  sense.  Diogenes  and  Johnson  reply,  practically, 
that  sense  contradicts  reason  ;  which  is  ignoratio  clcncki.7 

a  Hansel's  note  in  Aldricli,  Appendix,  §  5,  1.  Cf.  Plato,  Parmenides,  p.  128; 
Aristotle,  De  Soph,  x,  2,  and  xxxiii,  4 ;  and  Cousin,  Nouvcaux  Fragmens,  Zenon 
d'ffle.  8Zc*7w,p.411. 

4  Epist.  pt.  i,  Ep.  118.  6  Friend,  vol.  iii,  p.  93.  6  Logic,  p.  168. 

7  The  four  principal  arguments  with  which  Zeno  proposed  to  disprove  the  re- 
ality of  motion  are  as  follows : 


\ 


298  OF    FALLACIES. 

§  3.  The  Diodorus  Cronus  is  so  called  from  the  name  of  its  invent- 
or.8 It  also  professes  to  demonstrate  the  impossibility  of  motion. 
It  ranks  high  among  the  Inexplicables,  and  has  probably  been  more 
discussed  than  any  other  puzzle  on  record.  It  is  as  follows : 

If  motion  is  possible,  a  body  moves  either  in  the  place  where  it  is,  or  in  the  place 

where  it  is  not ; 
But  it  cannot  move  in  the  place  where  it  is,  for  there  is  not  room ;  nor  in  the 

place  where  it  is  not,  for  it  is  not  there  to  move,  and  nothing  can  act  or 

suffer  where  it  is  not ; 
.'.  Motion  is  impossible. 

The  story  goes  that  Diodorus  had  reason  to  lament  this  brilliant  in- 
vention. He  sent  for  a  surgeon  to  reset  his  dislocated  shoulder,  who, 
instead  of  setting  it,  set  himself  to  prove  by  this  same  irrefutable 
logic  that  dislocation  was  impossible. 

Formally  the  reasoning  is  quite  correct.  It  is  a  conjunctivo-dis- 
junctive  syllogism,  treated  conjunctively  in  the  tollent  mood.  But 
the  major  premise  is  false. 

First,  the  disjunction  is  not  contradictory.  "The  place  where  a 
body  is  "  is  contradictory  of  "  the  place  where  it  is  not ;"  but  "  moves 
in  a  place  where  it  is "  is  not  contradicted  by  "  moves  in  a  place 
where  it  is  not,"  but  rather,  as  it  should  be,  by  "  does  not  move  in 
a  place  where  it  is."  If  so  stated,  the  same  conclusion  could  not  be 
formally  drawn,  for  then  the  consequent  could  not  be  totally  denied 
on  the  grounds  adduced  in  the  minor. 

Secondly,  we  cannot  view  the  disjunction  as  merely  incomplete,  re- 
quiring a  tertium  quid  to  complete  it,  and  therefore  inept;  for  the 
second  member,  "moves  in  a  place  where  it  is  not,"  cannot  be  accepted 
at  all ;  it  is  a  self-contradiction,  or  a  mere  jumble  of  words,  a  bit  of 
sheer  nonsense. 

1.  Motion  cannot  begin,  because  a  body  in  motion  cannot  arrive  at  another 
place  until  it  has  passed  through  an  unlimited  number  of  intermediate  places. 

2.  Achilles  cannot  overtake  the  tortoise,  because  as  often  as  he  reaches  the  place 
occupied  by  the  tortoise  at  a  previous  moment,  the  latter  has  already  left  it. 

3.  The  flying  arrow  is  at  rest ;  for  it  is  at  every  moment  in  only  one  place. 

4.  The  half  of  a  division  of  time  is  equal  to  the  whole ;  for  the  same  point, 
moving  with  the  same  velocity,  traverses  an  equal  distance  (i.  e.,  when  compared, 
in  the  one  case,  with  a  point  at  rest,  in  the  other  with  a  point  in  motion),  in  the  one 
case,  in  half  of  a  given  time,  in  the  other  in  the  whole  of  that  time. 

For  interesting  historical  notices  concerning  these  famous  arguments,  see  Ueber- 
weg's  Hist,  of  Phil.  §  20. 
"Diog.  Laert.  ii,  112. 


EXAMPLES.  299 

Thirdly,  the  first  disjunct  member  is  rendered  absurd  by  an  inaccu- 
rate use  of  the  preposition  "  in."  A  body  cannot  be  thought  as  mov- 
ing "  in  a  place,"  in  situ.  This,  also,  is  essentially  a  self-contradiction, 
an  incongruous  use  of  words.  A  body  can  only  be  thought  as  mov- 
ing/row the  place  in  which  it  was,  through  the  place  iu  which  it  is, 
into  the  place  where  it  is  about  to  be.  This  objection  was  raised  by 
Gassendi,  and  is  repeated  by  De  Morgan.9 

Mansel  considers  the  disjunction  as  incomplete,  as  omitting  a  third 
horn,  the  possibility  of  "  moving  partly  in  a  place  where  it  is,  and 
partly  in  a  place  where  it  is  not ;"  and  therefore  he  rejects  the  major 
premise.  The  same  solution,  substantially,  is  given  by  Hobbes.10  But 
I  cannot  clearly  understand  what  is  meant  by  a  body's  "  moving  partly 
in  a  place  where  it  is  not."  Hobbes,  however,  undertakes  to  prove 
with  a  diagram  that  a  body,  quantulumcunque  sit,  however  small  it 
may  be,  "cannot  all  at  once  so  leave  the  whole  of  its  former  place 
that  a  part  of  it  shall  not  be  in  that  portion  which  is  common  to  the 
two  places,  namely,  the  one  which  is  left  and  the  other  which  is 
reached."  This  is  merely  an  evasion ;  for  a  part  of  a  body  is  itself  a 
body,  to  which  the  sophism  still  applies.  Or  it  may  be  considered  as 
an  attempt  to  solve  the  difficulty  metaphysically,  involving  the  question 
concerning  the  infinite  divisibility  of  matter. 

Bo  wen  refers  the  sophism  to  F.  accidentis"  and  supplies  the  omitted 
limitation  thus :  "  A  moving  body,  at  o.ny  one  indivisible  moment,  must 
be  either  where  it  is  or  where  it  is  not.  Hence,  in  any  one  indivisible 
moment  motion  is  impossible,  for  motion  requires  time  as  well  as 
space.  When  the  proviso  here  italicized  is  expressed,  the  proposition 
is  true,  the  reasoning  is  sound,  and  the  conclusion  correct."  I  am 
still  partially  in  the  dark.  What  does  he  mean  by  the  second  mem- 
ber of  the  disjunction,  "  or  it  must  be  where  it  is  not?" 

§  4.  The  Litigiosus,  or  Reciprocus,  is  a  noted  dilemma  of  which  we 
have  two  accounts,  one  Greek  ia  and  one  Roman.13  The  latter  tells  it 
of  Protagoras,  the  prince  of  sophists,  and  Euathlus,  his  pupil  in  the 
law.  Euathlus  had  contracted  to  pay  his  tuition  fee  when  he  gained 

9  Formal  Logic,  p.  260.  10  Philosophia  Prima,  pt.  ii,  ch.  viii,  §11. 

nZo^,p.298. 

18  By  Suidas,  in  Waltz's  Rhctores  Greed,  vol.  iv,  p.  13,  where  it  is  told  of  Corax 
and  Tisias ;  and  thence  is  said  to  have  originated  the  proverb,  KOJCOV 
KCIKOV  MOV,  which  in  part  still  survives  among  the  vulgar  of  to-day. 

13  Aulus  Gcllius,  bk.  v,  ch.  x. 


300  OF    FALLACIES. 

his  first  case.     But  not  having  any  case,  he  was  finally  sued  for  the 
fee  by  Protagoras,  who,  in  court,  addressed  him  thus : 

"  Learn,  most  foolish  of  young  men,  that,  however  matters  may  turn  out,  pay  me 
my  demand  you  must.  For  if  the  judgment  be  against  you,  I  shall  obtain  the  fee 
by  decree  of  the  court ;  and  if  in  your  favor,  by  the  terms  of  our  contract,  for  then 
you  shall  have  gained  your  first  case." 

To  this  Enathltis,  proving  at  least  that  he  was  an  apt  pupil,  replied 
in  corresponding  terms,  as  follows : 

"  Most  sapient  of  masters,  learn  from  your  own  argument  that,  whatever  may  be 
the  finding  of  the  court,  absolved  I  must  be  from  any  claim  of  yours.  For  if  the 
decree  be  in  my  favor,  I  shall  accordingly  pay  nothing ;  and  if  adverse,  I  shall  pay 
nothing  by  virtue  of  the  contract,  for  I  shall  not  have  gained  my  first  case." 

The  perplexed  judges,  unable  to  find  a  ratio  decidendi,  adjourned 
the  case  sine  die. 

The  dilemmas  are  the  same.  The  disjunction  is  incomplete.  The 
omitted  member  is  "  no  decree  at  all."  Protagoras  had  no  ground 
for  suit,  and  the  judges  should  have  quashed  the  case  with  a  nolle 
pros.  Practically  this  was  the  result. 

§  5.  The  Mcntiens,  classed  of  old  among  the  Insolubilia,  and  known 
to  the  Greeks  by  the  title  tyevdonevog,  was  also  invented  by  Eublides. 
Chrysippus,  the  Stoic,  wrote  six  treatises  on  it,  and  Philetas  of  Cos,  it 
is  said,  studied  himself  to  death  in  the  vain  attempt  to  solve  it.14 
Cicero  states  it  thus  : 

^  "If  you  say  that  you  lie,  and  say  so  truly,  then  you  do  lie;  but  if  you  say  so 
falsely,  then  you  speak  the  truth.  The  same  assertion,  therefore,  is  at  once  false 
and  true."  15 

"The  solution,"  says  Mansel,16  "is  very  obvious.  No  one  can  lie 
without  lying  about  something.  The  statement  '  I  lie,'  taken  alone, 
is  senseless."  But  it  seems  we  are  to  understand  that  "  I  lie  in  this 
very  statement  that  I  lie."  Then  it  would  be  more  formally  logical  to 
say  that  this  statement,  being,  like  all  other  assertions,  primarily  offer- 
ed as  true,  is  a  logical  paradox,  a  self-contradiction,  destroying  itself, 
and  therefore  null.  Gassendi  puts  the  sophism  thus :  "  Qui  jurat  se 
\  falsum  jurare  et  falsum  jurat,  vere  jurat." 


14  Diog.  Lacrt,  7,  §  196.  15  Acad.  Qucest.  iv,  30. 

16  Note  in  Aldrich,  Appendix,  §  6,  4. 


EXAMPLES.  301 

Let  us  take  tins  occasion  to  speak  once  again,  and  more  generally, 
of  the  logical  paradox.17  A  self-contradiction  in  terms  is,  of  course,  a 
blunder  in  dictione,  as  in  the  following  examples : 

Human  thought  is  bounded  only  by  the  infinite. 

Let  us  compel  them  to  volunteer. 

The  crime  of  suicide  deserves  capital  punishment. 

There  are  many  kinds  of  individuals. 

It  is  better  not  to  know  so  much  than  to  know  so  many  things  that  aren't  so. 

But  sometimes  the  paradox  is  extra  dictionem,  and  not  quite  so  ob- 
vious. Suppose  we  say  of  a  man  that  he  is  always  a  liar.  If  this  be 
true,  then  he  can  never  say  or  imply  "  I  lie,"  for  this  would  be  telling 
the  truth.  But  since  we  must  think  that  any  man  may  say  this,  it 
follows  that  "a  man  always  a  liar"  is  an  impossible  conception,  it 
is  a  self-contradiction.  " Hoc  unum  scio,  quod  nihil  scio"  Socrates  is 
reported  to  have  said.  "  It  is  certain  that  there  is  nothing  certain," 
said  the  paradoxical  philosophers  of  the  Middle  Academy.  This  say- 
ing Pyrrho,  the  Sceptic,  disputed  thus :  "  Everything  is  so  uncertain 
that  it  is  even  doubtful  whether  there  be  nothing  certain."  But  this 
absolute  scepticism  of  "  those  who  doubt  that  doubt  itself  is  doubt- 
ing "  involves  also  a  self-contradiction  ;  it  professes  a  belief  that  there 
is  no  belief.  Of  all  universal  propositions,  it  has  been  said,  one  only 
/  is  allowable,  In  generalibus  latet  error:  this  denies  all  others;  and 
then,  when  closely  looked  at,  it  too  commits  suicide. 

Recurring  once  more  to  the  remark  that  jests  arc  generally  fallacies, 
we  add  that  the  essence  of  the  "Irish  bull"  is  self-contradiction. 
Though  perhaps  not  half  the  lies  they  tell  of  the  Irish  are  true,  yet 
bulling  seems  a  natural  art  with  them,  and  not  intentional  mistake. 
Bulls  are  jests  in  earnest.  The  Paddy  who  said  he  was  not  dead,  but 
only  speechless,  was  a  living  felo  de  se,  and  typical  of  the  isle  whose 
overflowing  cup  of  woe  is  not  yet  full,  asking  only  for  non-interference, 
and  for  but  little  of  that. 

§  G.  The  Sorites  (vapor),  a  heap,  is  attributed  by  Persius18  to  Chry- 
sippus  as  the  inventor,  but  Diogenes  Laertius  "  attributes  it  to  Eubli- 
des.  It  is  defined  by  Ulpian  as  a  sophism  in  which  by  very  small  de- 
grees the  respondent  is  brought  from  the  evidently  true  to  the  evident- 
ly false.  For  example,  I  ask,  Does  one  grain -of  corn  make  a  heap? 
No.  Do  two  grains  make  a  heap  ?  No.  Do  three  grains  ?  No.  And 

17  See  Part  1st,  ii,  §  3.  "  Satires,  vi,  80.  "  Bk.  ii,  §  108. 


302  OF   FALLACIES. 

V  so  on,  adding  each  time  a  single  grain,  until  at  last  the  respond- 
ent is  forced  to  say  that  the  total  reached  does  make  a  heap.  I  then 
charge  him  with  saying  that  a  single  grain  makes  all  the  difference  be- 
'  tween  what  is  and  what  is  not  a  heap,  which  is  absurd. 

This  reasoning,  as  applied  to  various  objects,  is  called  by  various 
names.  Besides  Sorites,  which  Cicero 20  renders  by  Acervalis,  we  have 
the  Crescens,  the  Superpositus,  the  Calvus,  and  others.  This  last  name 
is  derived  from  the  exemplum  of  Eublides,  wherein  the  series  of  ques- 
y  tions  begins  with  asking  whether  pulling  one  hair  from  a  man's  head 
makes  him  bald.  The  sophism  is  used  by  Horace21  to  ridicule  the 
fashion  of  valuing  authors  merely  for  their  antiquity.  The  name  So- 
rites does  not  occur  in  Aristotle.  After  him,  it  was  used  by  the  an- 
cients, but  only  as  a  designation  of  the  above  sophism.  About  the 
middle  of  the  fifteenth  century  it  came  to  be  applied  also  to  the  chain 
syllogism,28  between  which  and  this  ancient  sophism  there  exists  no 
analogy  whatever.23 

In  explanation  of  the  sophism,  Krug  says,24  "  It  attempts,  from  the 
impossibility  of  assigning  the  limit  of  a  relative  notion,  to  show,  by 
continued  interrogation,  the  impossibility  of  its  determination  at  all. 
There  are  certain  notions  which  are  conceived  only  as  relative,  as  pro- 
portional, and  whose  limits  we  cannot,  therefore,  assign  by  the  gradual 
addition  or  detraction  of  one  denomination.  But  it  does  not  follow 
that,  if  a  notion  cannot  be  determined  in  this  manner,  it  is  incapable 
of  any  determination,  and  therefore  null."  This  explanation  is  adopt- 
ed by  Hamilton.25  The  sophism,  in  this  view,  is  evidently,  as  to  form, 
a  fallacy  of  definition. 

§  7.  The  Ignava  ratio  (ayoe  Ao'yoc)  is  commonly  attributed  to  the 
Stoics,  by  whom  it  was  employed  in  support  of  their  doctrine  of  fate.26 
It  is  propounded  by  Cicero27  in  the  form  of  a  complex  constructive 
dilemma;  thus: 

If  it  be  fated  that  you  recover  from  your  present  disease, 

then,  whether  you  call  in  a  doctor  or  not,  you  will  recover ; 
and  if  it  be  fated  that  you  do  not  recover, 

then,  whether  you  call  in  a  doctor  or  not,  you  wi1:!  not  recover. 
But  it  is  fated  either  that  you  recover,  or  that  you  do  not  recover. 
.*.  It  is  useless  to  call  in  a  doctor. 

30  De  Divinatione,  ii,  4.  S1  Epist.  ii,  1,  43  sq.  a3  Part  4th,  iv,  §  3. 

23  See  Hamilton's  Logic,  pp.  267-69.          21  Logik,  §  177.          »  Logic,  p.  332. 
88  This  origin  is  questioned  by  Hamilton,  Logic,  p.  331.          "  De  Fato,  ch.  xii. 


EXAMPLES.  303 

The  strictly  logical  conclusion  drawn  from  these  premises  would  be, — 
.'.  Whether  you  call  in  ,1  doctor  or  not,  you  will,  or  you  will  not,  recover. 

This  amounts  to  nothing.     The  dilemma  is  badly  formulated.     Let 
us  redress  it,  and  in  more  general  terms;  thus: 

If  an  event  is  fated  to  be,  ray  effort  is  useless ; 

and  if  it  is  fated  not  to  be,  my  effort  is  useless. 
But  it  is  fated  either  to  be  or  not  to  be. 
.'.  My  effort  is  useless. 

This  is,  in  form,  a  simple  constructive  dilemma,  and  logically  sound. 

The  ancient  idea  of  fate  is  the  ground  of  this  argument  for  inaction. 
It  considered  all  future  events  as  pre-established,  fixed  by  an  inevitable 
necessity,  by  a  destiny  originating  independently  of  divine  will  and  be- 
yond divine  control,  so  that  not  only  nature  and  man,  but  the  gods 
themselves,  were  subject  to  its  unalterable  decrees.  An  event  that  is 
fated  to  be  will  inevitably  be,  regardless  of  any  second  causes  that 
may  concur  to  counteract  or  modify  its  order.  "  If  this  doctrine  were 
true,"  says  Cicero,  "  life  would  be  reduced  to  a  state  of  hopeless  in- 
activity, and  the  above  argument  would  prove  the  inutility  of  any  en- 
deavor to  bring  about  a  desirable  result  or  to  avert  a  threatened  ca- 
lamity." Fate  was  personified  by  the  Greeks  in  the  Parca? ;  the  im- 
personal doctrine  prevailed  in  the  rest  of  the  ancient  world.  It  has 
barely  survived  with  the  Turks,  who,  as  fatalists,  will  not  take  precau- 
tions against  pestilence,  and  who  have  suffered  Constantinople  to  be 
repeatedly  destroyed  by  fire  without  an  effort  to  stay  the  conflagra- 
tion. It  need  hardly  be  said  that  there  is  no  such  thing  as  fate,  per- 
sonal or  impersonal.  It  is  a  vain  and  vague  imagining,  without  ground 
in  fact  or  reason. 

Necessitarians  of  the  present  day  do  not  argue  in  the  above  form. 
Their  doctrine  admits  the  contingency  of  second  causes;  but  these 
are  determined  and  determining.  "  There  is  no  thing  produced,  no 
event  happening,  in  the  known  universe  which  is  not  connected  by 
a  uniformity  or  inevitable  sequence  with  some  one  or  more  of  the 
phenomena  which  preceded  it.  These  antecedent  phenomena,  again, 
were  connected  in  a  similar  manner  with  some  that  preceded  them, 
and  so  on.  All  the  phenomena  of  nature,  then,  are  the  necessary,  or, 
in  other  words,  the  unconditional,  consequences  of  some  former  collo- 
cation of  causes.  The  state  of  the  whole  universe,  at  any  instant,  is 
the  consequence  of  its  state  at  the  previous  instant.  If  one  knew  all 
the  agents  which  exist  at  the  present  moment,  and  the  laws  of  their 


304  OF   FALLACIES. 

agency,  lie  might  predict  the  whole  future  history,  of  the  universe." a8 
This  doctrine  excludes  human  liberty,  and,  if  pushed  to  its  logical  re- 
sults, does  not  differ  essentially  from  fatalism. 

The  controversy  between  Liberty  and  Necessity  has  continually  agi- 
tated the  world,  in  one  form  or  another,  from  most  ancient  times. 
No  controversy  is  more  ancient,  none  more  universal,  none  has  more 
keenly  excited  the  minds  of  men,  none  has  exerted  a  greater  influence 
on  morals ;  it  has  divided  not  only  schools,  but  nations,  and  has  mod- 
ified not  only  their  opinions,  but  their  manners,  customs,  religion, 
and  government.  Under  its  influence  the  Ignava  ratio  has  taken 
many  forms,  been  applied  to  various  matter,  and  received  a  variety  of 
names.  Among  these  are :  De  fato,  Metens  (the  reaper),  De  possibi- 
libus,  De  libero  arbitrio,  De  providentia,  De  divinis  decretis,  De  futu- 
ris  contingentibus,  De  physica  prcedeterminatione,  etc.  We  are  here 
concerned  with  the  argument  only  in  the  form  given  above. 

The  subsuraption  is  false.  Let  us  examine  it.  What  is  meant  by 
"an  event  fated  to  be?"  The  essential  idea  of  "fated"  is  "inevita- 
ble," that  is,  not  modified  by  any  precedent  or  concurrent  events, 
substantially  and  personally  expressed  by  "  regardless  of  my  effort." 
So  our  personal  argument  reduces  to  : 

If  an  event  is,  regardless  of  my  effort,  to  be, 

my  effort  is  useless ; 
and  if  it  is,  regardless  of  my  effort,  not  to  be, 

my  effort  is  useless. 
But  every  event  is,  regardless  of  my  effort, 

either  to  be  or  not  to  be. 
.*.  All  my  effort  is  useless. 

Now,  consider  this  subsumption.  Who  can  affirm  it  ?  What  ground 
has  it  ?  It  may  be  true  of  some  event,  as  an  eclipse,  that  I  can  neither 
effect  it  nor  affect  it ;  and  of  it  we  may  say  that  it  must  either  take 
place  from  other  causes  or  not  at  all.  But  many  events  depend 
wholly  or  in  part  upon  my  effort  as  a  conditio  sine  gua  non.  The 
only  real  fate  is  a  concurrence  of  causes,  an  assemblage  of  conditions. 
Supply  a  new  cause,  take  away  one  of  the  necessary  conditions,  and 
the  result  will  be  different,  though  still,  if  you  please  to  call  it  so,  a 
fated  or  necessary  result.  Fate  changes  then  her  decree.  Sending 
for  a  doctor  introduces  a  new  cause;  neglecting  to  send  may  be  the 
omission  of  a  condition  necessary  to  recovery. 

88  Mill's  Logic,  p.  250. 


EXAMPLES.  305 

If  the  necessitarian  objects  that  my  will  is  itself  determined  by  prior 
causes,  I  reply  that  then,  it  may  be,  I  am  fated  to  send  for  a  doctor, 
and  so  to  recover ;  or  may  be  fated  not  to  send,  and,  as  a  consequence 
of  this  neglect,  fated  to  die.  So  my  effort  is  not  useless,  not  inconse- 
quent. Zeno,  the  Stoic,  who  adopted  the  argument,  once,  it  is  said, 
conceded  this.  He  undertook  to  flog  his  slave  for  theft,  who  aptly 
pleaded  that  he  was  fated  to  steal.  "  And  I  to  flog  you,"  was  the  reply. 

§  8.  Praxis.  Among  the  following  miscellaneous  examples  are 
some  cases  of  good  reasoning  from  true  premises,  and  others  from 
false  premises,  as  well  as  fallacies  proper.  If  the  reasoning  is  sound, 
give  the  mood;  if  not,  analyze  the  thought,  indicate  the  logical  de- 
fect, and  name  the  species  of  fallacy. 

1.  A  legitimate  argument  may  fail  to  win  assent;  *S 
No  fallacy  is  a  legitimate  argument ; 

/.  No  fallacy  can  fail  to  win  assent. 

2.  Whatever  represses  the  liberties  of  mankind  ought  to  be  resisted ; 
Among  those  things  that  do  so,  there  are  governments ; 

.*.  Governments  ought  to  be  resisted. 

3.  Every  one  desires  happiness ; 
Virtue  secures  happiness ; 

.*.  Every  one  desires  virtue. 

4.  Idolatry  is  wicked ; 

Wickedness  should  be  punished  by  law  ; 
.*.  Law  should  punish  idolatry. 

5.  Christianity  cannot  be  proven  true  by  its  success, 

for  Mohammedanism  has  succeeded ;      \ 
Nor  can  it  be  proven  by  its  alleged  miracles, 

for  Buddhism  has  its  alleged  miracles ; 
.*.  Christianity  cannot  be  proven  to  be  true. 

6.  We  ought  to  give  one  day  in  seven  to  religious  duties, 

if  the  fourth  commandment  is  obligatory  upon  us ; 
But  we  ought  thus  to  devote  one  day  in  seven ; 
/.  The  fourth  commandment  is  obligatory  upon  us. 
V.  We  are  forbidden  to  kill ; 

Inflicting  capital  punishment  is  killing ; 
.*.  We  arc  forbidden  to  inflict  capital  punishment. 
8.  A  king  is  a  man.     Then  it  immediately  follows,  by  added  deter- 
minants, that  a  good  king  is  a  good  man. 

20 


306  OF   FALLACIES. 

9.  No  moral  principle  is  an  animal  impulse ; 

But  some  animal  impulses  are  principles  of  action ; 
.-.  Some  principles  of  action  are  not  moral  principles. 

10.  The  papists  would  be  aggrieved  if  the  penal  laws  against  them 

were  enforced ; 
But  these  are  not,  and  hence  they  have  no  reason  to  complain. 

11.  Nothing  is  better  than  wisdom; 
Dry  bread  is  better  than  nothing ; 

/.  Dry  bread  is  better  than  wisdom. 

12.  No  person  destitute  of  imagination  is  a  true  poet; 

Some  who  are  destitute  of  imagination  are  good  logicians. 
/.  No  true  poet  is  a  good  logician. 

1 3.  Some  practically  virtuous  men  are  necessitarians ; 

But  all  necessitarians  speculatively  subvert  the  distinction  between 

vice  and  virtue ; 
/.  Some  who  deny  the  distinction  are  practically  virtuous. 

14.  Interference  with  another  man's  business  is  illegal; 
Underselling  interferes  with  another's  business ; 

/.  Underselling  is  illegal. 

15.  Pestilence,  being  "a  visitation  of  God,"  its  event  is  not  deter- 

mined by  physical  causes. 

1 3.  No  one  desires  to  do  wrong  if  cognizant  of  its  nature,  but  only  in 
consequence  of  ignorance ;  and,  therefore,  virtue  is  knowledge, 
and  is  to  be  attained  by  education ;  for  no  one  desires  evil  know- 
ing it  as  such,  and  to  do  wrong  is  evil. — From  Plato's  Gorgias. 

17.  His  imbecility  of  character  might  have  been  inferred  from  his 

proneness  to  favorites;  for  all  weak  princes  have  this  failing. 

18.  Quod  tangitur  a  Socrate  illud  sentit; 
Columna  tangitur  a  Socrate ; 
Ergo,  Columna  sentit. 

19.  The  right  of  the  government  is  unquestionable;  therefore  we 

ought  to  obey  it. 

20.  Every  visible  object  that  does  not  decompose  light  is  seen  by  white 

light,  and  is  therefore  white ; 

A  black-board  is  a  visible  object  that  does  not  decompose  light. 
/.  A  black-board  is  white. 

21.  Any  form  of  government  that  excludes  the  people  from  political 

power  is  subject  to  violent  revolutions ; 

A  democracy  does  not  so  exclude  the  people,  and  therefore  is  not 
subject  to  violent  revolutions. 


EXAMPLES.  807 

22.  The  planets  are  seven ; 
Mercury  and  Venus  are  planets ; 

.*.  They  are  seven. 

23.  No  cat  has  two  tails ; 

Every  cat  has  one  tail  more  than  no  cat ; 
.*.  Every  cat  has  three  tails. 

24.  To  allow  every  man  freedom  of  speech  must  always  be,  on  the 

whole,  for  the  good  of  the  state ;  for  it  is  highly  conducive  to 
the  interests  of  the  community  that  each  individual  should  en- 
joy a  liberty,  perfectly  unlimited,  of  expressing  his  sentiments 
on  its  affairs. 

25.  Let  x=2,  and  y=r3.     Take  the  self-evident  equations  ax^ax 

and  ay^ay,  add  them  together  and  transpose  terms;  this  will 
give  ax— ax = ay — ay.     Dividing  by  a— a,  we  obtain  x=ry,  or 
2  =  3. 
s  26.  Mus  syllaba  est ; 

Mus  caseum  rodit ; 

Ergo,  syllaba  caseum  rodit. — /SVweca,  J2/?^.  48. 

27.  There  are  many  men  that  reason  exceeding   clear  and  rightly, 

who  know  not  how  to  make  a  syllogism ;  therefore,  Logic  is 
useless. — Locke. 

28.  If  all  testimony  to  miracles  is  to  be  admitted,  the  popish  legends 

are  to  be  believed ; 
But  they  are  not  to  be  believed ; 
.*.  No  testimony  to  miracles  is  to  be  admitted. 

29.  None  but  whites  are  civilized ; 
The  ancient  Germans  were  whites ; 

.*.  They  were  civilized. 

30.  Only  give  me  the  luxuries  of  life,  and  I  will  dispense  with  the 

necessaries. 

31.  Unless  Logic  professes  to  be  an  instrument  of  invention,  the  re- 

proach that  it  discovers  nothing  is  unfounded ; 
But  it  does  not  make  this  profession  ; 
.'.  The  reproach  is  unfounded. 

32.  Teacher, — "  What  is  conscience  ?" 

Smart  boy, — "Don't  know"  (=" unprepared"). 

Teacher, — "  Why,  conscience  is  something  within  you  that  tells 

you  when  you  have  done  wrong." 
Boy, — "  Oh,  yes ;  I  had  it  once,  and  they  had  to  send  for  the 

doctor." 


308  OF   FALLACIES. 

33.  All  these  exercises  will  fatigue  me ; 
This  itself  is  one  of  them ; 

.*.  It  will  fatigue  me. 

34.  A  grain  of  corn  does  not  make  a  heap ; 

\     A  hundred  (99  +  1)  is  made  by  one  grain ; 
.*.  A  hundred  is  not  a  heap. 

35.  What  is  no  uncommon  occurrence  may  reasonably  be  expected; 
To  gain  a  high  prize  in  a  lottery  is  no  uncommon  occurrence ; 

.-.  To  gain  a  high  prize  may  reasonably  be  expected. 

36.  My  hand  touches  the  pen ; 
The  pen  touches  the  paper ; 

.*.  My  hand  touches  the  paper. 

37.  The  minimum  visibile  is  the  least  magnitude  that  can  be  seen. 
\  No  part  of  it  alone  is  visible,  and  all  parts  must  affect  the  mind  in 

order  that  it  may  be  visible.     Hence  every  part,  though  invisible, 
must  affect  the  mind. — See  Hamilton's  Metaphysics,  p.  243. 

38.  Improbable  events  happen  every  day ; 

J    But  what  happens  every  day  must  be  a  very  probable  event ; 
.*.  Improbable  events  are  very  probable. 

39.  Omnis  equus  est  bestia ; 
Omnis  Justus  est  sequus ; 

.*.  Omnis  Justus  est  bestia. — Burgersdyck. 

40.  Nuisances  are  punishable  by  law ; 
\       A  noisy  dog  is  a  nuisance ; 

.*.  A  noisy  dog  is  punishable  by  law. 

41.  Ham.  There's  ne'er  a  villain  dwelling  in  all  Denmark, 

But  he's  an  arrant  knave. 

Hor.    There  needs  no  ghost,  my  lord,  come  from  the  grave 
To  tell  us  this. — Hamlet,  act  i,  sc.  v. 

42.  All  that  glitters  is  not  gold ; 
Tinsel  glitters ; 

.*.  Tinsel  is  not  gold. 

43.  Bishop  (inspecting  the  chancel)  to  Curate  (ritualistically  inclined), 

— "  I  am  sorry  to  see  that  you  have  placed  a  cross  over  the  al- 
tar "  (pointing  to  the  sign  deeply  cut  into  the  wood-work). 
\     Curate, — "  But  please  observe  we  have  not  placed  one  there,  but, 
on  the  contrary,  have  taken  one  away." — Punch. 

44.  Tu  es  qui  es ; 
Quies  est  requies ; 
Ergo,  Tu  es  requies. 


EXAMPLES.  309 

45.  What  would  be  the  consequence  should  an  irresistible  force  en- 
counter an  insurmountable  obstacle  ? 
Ans.— Compound  stationary  motion. 
40.  Is  Patrocles  your  brother,  Socrates  ? 

Yes,  he  is  my  half-brother,  the  son  of  my  mother,  but  not  of  my 

father. 

Then  he  is,  and  is  not,  your  brother. 
Not  by  the  same  father,  good  man ;  for  Cha3redemus  was  his 

father,  and  mine  was  Sophroniscus. 
Chajredemus,  then,  was  other  than  a  father  ? 
Yes,  than  mine. 
But  can  he  who  is  other  than  a  father  be  a  father?  or,  are  you 

the  same  as  a  stone  ? 
I  am  afraid  you  will  prove  me  so. 
Are  you  not,  indeed,  other  than  a  stone  ? 
I  am. 
And,  being  other  than  a  stone,  you  are  not  a  stone ;  and  being 

other  than  gold,  you  are  not  gold. 
Very  true. 

And  so  Chrcredemus,  being  other  than  a  father,  is  not  a  father. 
It  seems  he  is  not  a  father. 
At  least,  if  Chaeredemus  is  a  father,  then  Sophroniscus,  being  other 

than  a  father,  you,  my  Socrates,  are  fatherless. — Plato's  Euihy- 

demus,  §  26. 

47.  Who  is  most  hungry  eats  most; 
Who  eats  least  is  most  hungry ; 

/.  Who  eats  least  eats  most. 

48.  A  professional  school  ought  to  be  zealously  attended,  for  in  it  we 

specially  prepare  for  our  vocation ; 

This  school  is  not  professional,  for  in  it  we  do  not  specially  pre- 
pare for  business ; 
/.  This  school  need  not  be  zealously  attended. 

49.  There  is  no  rule  without  exceptions ; 
This  statement  is  itself  a  rule  ; 

.*.  This  statement  has  exceptions ; 
i.  e.,  There  are  rules  without  exceptions. 

50.  Now  is  no  part  of  time,  for  a  whole  is  composed  of  its  parts,  and 

time  is  not  composed  of  nows.  Time  is  either  past  or  future. 
The  former  no  longer  exists ;  the  latter  not  yet  exists.  There- 
fore time  has  no  existence. — Aristotle's  Physica,  iv,  10. 


310  OF   FALLACIES. 

51.  The  annexed  figure  is  a  square,  say  16  inches ; 

therefore  containing  16x16  =  256  square 
inches.  Cut  it  in  pieces  by  the  dividing 
Jines,  and  place  the  parts  in  position  so  as 
to  make  the  rectangle  whose  base  is  26 
inches  and  altitude  10  inches.  This  rec- 
tangle contains  10x26  =  2  60  square  inches. 
.-.256  =  260. 

52.  The  man  who  is  walking  away  from  me  does  not  grow  smaller ; 
But  what  I  see  grows  smaller ; 

.-.  What  I  see  is  not  the  man. — Hume. 

53.  If  the  blest  in  heaven  have  no  desires, 

they  will  be  perfectly  content ; 
and  so  will  they  if  their  desires  are  fully  gratified. 
But  either  they  will  have  no  desires, 

or  they  will  have  them  fully  gratified. 
.-.  They  will  be  perfectly  content. 

54.  Knowledge  is  power ; 
Power  is  desirable ; 

.-.  Knowledge  is  desirable. 

55.  Qui  sunt  domini  sui  sunt  sui  juris; 
Servi  sunt  domini  sui ; 

Ergo,  Servi  sunt  sui  juris. 

56.  The  acute  metaphysician  Bishop  Berkeley  boasted  that  he  had 

\forever  put  an  end  to  "  scepticism,  atheism,  and  irreligion  "  by 
the  following  demonstration  of  the  existence  of  an  Eternal 

Mind,  of  God : 

Ideas  cannot  exist  without  a  mind  in  which  they  inhere. 
I  have  the  same  idea  to-day  that  I  had  yesterday. 
But  this  would  be  impossible  unless  there  were  a  mind  in  which 

it  existed  during  the  interval. 
Hence  there  must  exist  a  Universal  Mind  in  which  all  ideas  have 

their  permanent  residence  during  the  interval  of  their  conscious 

presence  in  our  own  minds. 

57.  Whoever  thrusts  a  knife  into  another  person  commits  an  injury. 

A  surgeon  does  this ;  therefore  he  commits  an  injury. 

58.  Ein  Weib  nur  zu  besitzen  ist  seiner  Leidenschaft  Ziel. — fries,  §  109. 

59.  A  magistrate  is  justified  in  using  his  official  power  to  forward  his 

religious  views,  because  every  man  has  a  right  to  inculcate  his 
own  opinions. 


^ 

EXAMPLES.  ''        311 

CO.  Quod  est  bonum,  omne  laudibile  est ; 

Quod  autem  laudibile  est,  omne  honestum  est ; 
Bonum  igitur  quod  est,  honestum  est.39 

61.  Prayer  may  be  regarded  as  useful,  if,  indeed,  we  can  regard  our 

prayers  as  announcing  to  Deity  what  he  does  not  know,  or  as 
changing  his  purposes. 
But  we  cannot  tell  the  Omniscient  what  he  does  not  already  know, 

nor  change  his  eternal  purposes. 
.*.  Prayer  is  useless. 

62.  Do  you  know  your  own  father  ?     Yes. 

Do  you  know  this  man  who  is  veiled  ?     No. 
Then  you  do  not  know  your  father ;  for  it  is  he.30 

63.  "The  Cretians  are  alway  liars." — Epistle  to  Titus,  i,  12. 
Epimenides,  who  said  this,  was  himself  a  Cretian,  and  "  this  wit- 
ness is  true." — Ibid. 

If  so,  Epimenides  himself  was  always  a  liar,  and  this  witness  is 
not  true. 

64.  Quand  la  terre  est  humide,  il  se  forme  de  la  vapeur,  et  par  suite 

de  la  vapeur,  un  nuage ;  et  par  suite  du  nuage,  de  la  pluie ;  par 
suite  de  la  pluie,  1'humidite  de  la  terre :  mais  ceci  est  precise- 
ment  le  point  de  depart,  et  1'on  y  est  revenu  circulairemcnt 
(/cy^Xw  7TEpi£\ri\vd£v). — Saint-Hilaire,  Comment,  t.  i,  p.  524. 

65.  Predestination  makes  man  immoral ;  for  if  a  man  be  an  heir  of 

grace,  his  exertions  are  useless  ;  if  of  wrath,  unavailing. 

But,  according  to  predestination,  a  man  is  an  heir  either  of  grace 
or  of  wrath ; 

Therefore,  according  to  predestination,  his  exertions  must  be  use- 
less. 

But  he  who  believes  his  exertions  to  be  useless  must  be  immoral ; 

Therefore  predestination  makes  man  immoral. — Macaulay. 

66.  The  gods,  said  the  Epicureans,  are  very  happy ; 
None  can  be  happy  without  virtue ; 

There  is  no  virtue  without  reason  ; 

Reason  is  found  nowhere  except  in  human  form ; 

Therefore,  the  gods  have  human  form. 


29  A  Stoical  argument,  from  Cicero's  De  Finibus,  bk.  iii. 

30  Obvdatus,  or  Occult,by  Eublides  of  Megara.  —  Diog.  Laert.  ii,  §  108.      Also 
called  Elcctra,  from  Sophocles,  Elect.  1222.     See  De  Soph.  24,  2 ;  and  a  cursory  re- 
view of  Aristotle's  solution  in  Grote's  Aristotle,  vol.  ii,  p.  119  sq. 


312  OF   FALLACIES. 

67.  There  is  no  such  thing  as  a  void ;  for  in  a  void  there  could  be  no 

difference  of  up  and  down ;  for  as  in  nothing  there  are  no  dif- 
ferences, so  there  are  none  in  privation  or  negation.  But  a  void 
is  merely  a  privation  or  negation  of  matter.  Therefore,  in  a 
void,  bodies  could  not  move  up  and  down,  which  it  is  in  their 
nature  to  do. — Aristotle's  Physica. 

68.  The  doctor  who  attended  Pat's  wife  in  her  last  illness  afterwards 

had  to  sue  him  for  the  fee.  The  court  gave  Pat  permission  to 
question  him.  "  Docthor,  didn't  ye  agree  that, '  kill  or  cure,'  ye 
would  charge  me  only  a  guinea?"  "Yes."  "  Well,  docthor, 
did  ye  cure  her?"  "No,  she's  dead."  "Well,  docthor,  did 
\  ye  kill  her  ?"  "  No,  surely."  "  Thin,  docthor,  if  ye  did  naither, 
how  can  ye  ask  a  fee  ?" 

69.  Themistoclis  films  nee  Gra?.cis  imperat,  nee  de  imperando  cogitat. 

Verum  imperat  matri,  qua3  imperat  Themistocli,  qui  Graecis 
imperat.  Dominatur  itaque  Grsecis,  et  non-dominatur.31 

70.  If  the  wife  you  espouse  be  beautiful,  she  excites  jealousy ; 
If  she  be  ugly,  she  disgusts ; 

Therefore  it  is  best  not  to  marry.— Bias,  quoted  by  Aldus  Gellius. 

71.  A  sailor  is  not  a  board,  nor  is  a  sailor  a  shore ; 
But  always  he  is  either  aboard  or  ashore ; 

/.  A  sailor  is  not  a  sailor. 

72.  A  desire  to  gain  by  another's  loss  is  a  violation  of  the  tenth  com- 

mandment. All  gaming,  therefore,  since  it  implies  a  desire  to 
profit  at  the  expense  of  another,  breaks  this  commandment. 

73.  He  that  is  of  God  heareth  God's  words;  ye,  therefore, hear  them 

not,  because  ye  are  not  of  God. — John  viii,  47. 

74.  If  Abraham  were  justified  by  works,  then  he  had  whereof  to  glory 

(before  God).  But  not  (any  one  can  have  whereof  to  glory)  be- 
fore God  (therefore,  Abraham  was  not  justified  by  works). — 
Romans,  iv,  2. 

75.  What  is  of  less  frequent  occurrence  than  the  falsity  of  testimony 

cannot  be  established  by  testimony  ; 

Miracles  are  of  less  frequent  occurrence  than  the  falsity  of  testi- 
mony ; 
/.  Miracles  cannot  be  established  by  testimony. — Hume. 

31  This  famous  "  Inexplicable  "  is  called  Dominam,  or  Kvpievuv.  It  is  mentioned 
by  Plutarch,  Arrian,  Lucian,  Gellius,  and  others,  but  not  fully  explained  by  any. 
For  a  discussion  of  it,  see  Butler's  Lectures  on  Ancient  Philosophy,  i,  p.  414 ;  and 
Hansel  in  Aldrich,  Appendix,  §  9. 


EXAMPLES.  313 

76.  Exemption  from  punishment  is  due  to  the  innocent ;  therefore,  as 

you  maintain  that  the  prisoner  at  the  bar  ought  not  to  be  pun- 
ished, it  appears  that  you  maintain  his  innocence. 

77.  In  Platon's  Euthydcmos  kommt  dieses  vor :  Hast  du  einen  Hund  ? 

Ja.  Hat  er  Junge?  Ja.  1st  er  der  Vater  der  Jungcn?  Ja. 
Also  ist  dcin  Hund  em  Vater,  und  folglich  dcin  Vater  cm  Hund. 
— Fries,  §  109.  Cited  also  in  De  Soph.  xxiv. 

78.  If  men  are  not  likely  to  be  influenced  in  the  performance  of  a 

known  duty  by  taking  an  oath  to  perform  it,  the  oaths  com- 
monly administered  are  superfluous;  if  men  are  likely  to  be  so 
influenced,  every  one  should  be  made  to  take  an  oath  to  behave 
rightly  throughout  his  life.  But  one  or  the  other  of  these 
must  be  the  case.  Therefore,  either  the  oaths  commonly  ad- 
ministered are  superfluous,  or  every  man  should  be  required 
to  take  an  oath  to  behave  rightly  throughout  his  life. — 
Whately. 

79.  The  principles  of  justice  being  variable,  and  the  appointments  of 

nature  invariable,  it  follows  that  the  principles  of  justice  are  no 
appointment  of  nature. — Aristotle's  Ethics,  bk.  iii. 

80.  If  the  favor  of  God  is  not  bestowed  at  random,  on  no  principle 

at  all,  it  must  be  bestowed  either  with  respect  to  men's  persons 
or  with  respect  to  their  conduct.  But  "  God  is  no  respecter  of 
persons."  Therefore  his  favor  must  be  bestowed  with  refer- 
ence to  men's  conduct. — Sumncr^s  Apostolical  Preaching. 

81.  Jupiter  was  the  son  of  Saturn,  therefore  the  son  of  Jupiter  was 

the  grandson  of  Saturn. 

82.  Two  straight  lines  cannot  enclose  a  space  (Axiom  x).     But  two 

parallel  straight  lines  of  infinite  length  do  enclose  an  infinite 
space.  Moreover,  if  a  third  line  parallel  to  these  be  drawn  mid- 
way between  them,  it  will  divide  this  infinite  space  into  two 
equal  parts,  each  of  which  is  one  half  of  infinity. 

83.  Opium  is  poison.     But  physicians  advise  some  of  their  patients 

to  take  opium.  Therefore,  physicians  advise  some  of  their  pa- 
tients to  take  poison. 

84.  "  The  knowledge  of  relatives  is  one."     I  cannot  be  conscious  of  a 

mental  act  without  being  conscious  of  the  object  to  which  that 
act  relates.  But  the  object  of  memory  confessedly  lies  in  the 
past,  and  has  ceased  to  be.  Therefore,  in  memory  I  am  con- 
scious of  an  object  in  the  past,  and  am  conscious  of  what  does 
not  exist. — See  Hamilton's  Metaphysics,  p.  146  sq. 


314  OF    FALLACIES. 

85.  Animal  food  may  be  dispensed  with,  for  the  vegetarians  do  not 

use  it ;  and  vegetable  food  may  be  dispensed  with,  for  the  Esqui- 
maux do  not  use  it. 

But  all  food  is  either  animal  or  vegetable. 
/.  All  food  may  be  dispensed  with. 

86.  No  soldiers  should  be  brought  into  the  field  but  those  who  are 

well  qualified  to  perform  their  part ; 

None  but  veterans  are  well  qualified  to  perform  their  part ; 
.-.  Veterans  only  should  be  brought  into  the  field. 

87.  We  can  attend  to  a  plurality  of  objects  at  once.     For  if  attention 

be  nothing  but  the  concentration  of  consciousness  on  a  smaller 
N  number  of  objects  than  constitute  its  widest  compass  of  simul- 
taneous knowledge,  it  is  evident  that,  unless  this  widest  compass 
of  consciousness  be  limited  to  only  two  objects,  we  do  attend 
when  we  converge  consciousness  on  any  smaller  number  than 
that  total  complement  of  objects  which  it  can  embrace  at  once. 
— Hamil tori's  Metaphysics,  p.  165. . 

88.  In  what  and  how  many  phrases  does  Hamilton,  in  his  "  immedi- 

ate demonstration  "  that  sight  is  cognizant  of  extension,  assume 
the  point  to  be  proved? — Ibid.,  p.  385. 

89.  It  would  be  bad  reasoning  in  an  Anabaptist  to  prove  against  the 

Catholics  that  they  are  wrong  in  believing  that  infants  are  ca- 
pable of  baptism,  since  nothing  is  said  of  it  in  the  Scripture ; 
because  this  proof  would  assume  that  we  ought  to  believe  only 
what  is  in  the  Scripture,  which  is  denied  by  the  Catholics. — 
Arnauld,  p.  251. 

90.  How  can  we  conceive  God,  since  we  can  attribute  no  virtue  to 

him  ?  For  shall  we  say  that  he  has  prudence  ?  But  since  pru- 
dence consists  in  the  choice  between  good  and  evil,  what  need 
can  God  have  of  this  choice,  not  being  capable  of  any  evil? 
Shall  we  say  that  he  has  intelligence  and  reason  ?  But  intelli- 
gence and  reason  serve  to  discover  to  us  that  which  is  unknown 
from  that  which  is  known  ;  now  there  can  be  nothing  unknown 
to  God.  Neither  can  justice  be  in  God,  because  this  relates 
only  to  the  intercourse  of  men  ;  nor  temperance,  since  he  has  no 
desires  to  moderate;  nor  strength,  since  he  is  susceptible  of 
neither  pain  nor  labor,  and  is  not  exposed  to  any  danger.  How 
therefore,  can  that  be  a  god  which  has  neither  intelligence  nor 
virtue  ? 32 

83  Cotta,  quoted  by  Cicero,  De  Natnra  Deorum,  bk.  iii. 


EXAMPLES.  315 

91.  That  which  has  the  use  of  reason  is  better  than  that  which  has  not; 
There  is  nothing'  better  than  the  universe ; 

.*.  The  universe  has  the  use  of  reason. — The  Stoics. 

92.  Why  does  a  ball,  when  dropped  from  the  mast-head  of  a  ship  in 

full  sail,  not  fall  exactly  at  the  foot  of  the  mast,  but  nearer  to 
the  stern  of  the  vessel  ? 

93.  Gold  and  silver  are  wealth ;  therefore  the  diminution  of  the  gold 

and  silver  of  the  country  by  exportation  is  a  diminution  of  the 
wealth  of  the  country. 

94.  If  man  be  not  a  necessary  agent  determined  by  pleasure  and  pain, 

there  is  no  foundation  for  rewards  and  punishments.  These 
would  be  useless  unless  men  were  necessary 'agents,  and  were 
determined  by  pleasure  and  pain ;  because  if  men  were  free  and 
indifferent  to  pleasure  and  pain,  pain  could  be  no  motive  to 
cause  them  to  observe  the  law. 

95.  It  is  certain  that  drunkenness  is  a  vice  odious  to  God  and  man. 

It  is  equally  certain  that  alcoholic  drinks  are  destructive  to  the 
moral,  intellectual,  and  physical  energies  of  him  who  habitually 
makes  use  of  them.  I  claim,  therefore,  not  only  that  it  is  the 
duty  of  every  man  to  abstain  totally  from  their  use,  but,  as  a 
good  citizen  and  philanthropist,  to  exert  all  his  influence  to  ob- 
tain and  enforce  a  law  prohibiting  the  sale  of  any  kind  of  in- 
toxicating beverages. 

96.  (Analyze  the  argument  of  Krug  and  the  reply  of  Biunde,  as  stated 

in  Hamilton's  Metaphysics,  pp.  565-66.) 

97.  Minus  multiplied  by  minus  cannot  give  minus ;  for  minus  multi- 

plied by  plus  gives  minus,  and  minus  multiplied  by  minus  can- 
not give  the  same  product  as  minus  multipled  by  plus. — Euler's 
Algebra.  See  Mill's  Logic,  p.  575. 

98.  "  Either  God  wills  to  remove  evils  and  cannot ;  or  he  can  and  will 
\      not;  or  he  neither  will  nor  can ;  or  he  both  will  and  can.    If  he 

will  and  cannot,  then  he  is  weak,  which  is  not  true  of  God.  If 
he  can  and  will  not,  then  he  is  malicious,  which  also  is  foreign 
to  the  nature  of  God.  If  he  neither  will  nor  can,  then  he  is 
both  malicious  and  weak,  and  therefore  cannot  be  God.  If  he 
both  can  and  will,  which  alone  is  consistent  with  the  nature  of 
God,  then  whence  are  evils,  or  why  does  he  not  remove 
them  ?" 33 

83  Epicurus,  quoted  by  Lactantius,  Be  Ira  Dei,  xiii. 


316  OF   FALLACIES. 

99.  The  doctrine  of  an  omnipresent  divine  power  and  agency  in  the 
operations  of  Nature  is  as  contrary  to  the  Scriptures  as  it  is  to 
sound  philosophy ;  for  the  Scriptures  say  expressly,  "  The  earth 
bringeth  forth  fruit  of  herself  "—Mark,  iv,  28. 

100.  If  a  reconciliation  between  the  ancient  historical  records  and 

modern  culture  be  sought  by  means  of  interpretation,  it  will 
be  attempted  to  prove  either  that  the  divine  did  not  manifest 
itself  in  the  manner  related,  which  is  to  deny  the  historical 
validity  of  the  ancient  Scriptures ;  or  that  the  actual  occur- 
rences were  not  divine,  which  is  to  explain  away  the  absolute 
contents  of  these  books.34 

101.  Do  but  let  the  Bible  tell  its  own  story;  grant,  for  the  sake  of 

argument,  the  truth  of  the  dogmas  which  it  asserts  throughout, 
and  it  becomes  a  consistent  whole.  When  a  man  begins,  as 
Strauss  does,  by  assuming  the  falsity  of  its  conclusions,  no 
wonder  he  finds  its  premises  a  fragmentary  chaos  of  contra- 
dictions.35 


34  D.  F.  Strauss,  in  Leben  Jesu,  Int.  §  1. 

35  Dean  Alton  Locke,  Works,  vol.  i,  ch.  xxxviii. 


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LOSSING'S  CYCLOPAEDIA  OF  UNITED  STATES  HISTORY.  From 
the  Aboriginal  Period  to  1876.  By  B.  J.  LOSSING,  LL.D,  Illustrated 
by  2  Steel  Portraits  and  over  1000  Engravings.  2  vols.,  Royal  Svo,  Cloth, 
$10  00.  (Sold  by  Subscription  onfy.) 

LOSSING'S  FIELD-BOOK  OF  THE  REVOLUTION.  Pictorial  Field- 
Book  of  the  Revolution  ;  or,  Illustrations  by  Pen  and  Pencil  of  the  Historv, 
Biography,  Scenery,  Relics,  and  Traditions  of  the  War  for  Independence. 
By  BENSON  J.  LOSSING.  2  vols.,  8vo,  Cloth,  $14  00 ;  Sheep  or  Roan, 
$15  00;  Half  Calf,  $18  00. 

LOSSING'S  FIELD-BOOK  OF  THE  WAR  OF  1812.  Pictorial  Field- 
Book  of  the  War  of  1812 ;  or,  Illustrations  by  Pen  and  Pencil  of  the  His- 
tory, Biography,  Scenery,  Relics,  and  Traditions  of  the  hist  War  for 
American  Independence.  By  BENSON  J.  LOSSING.  With  several  hun- 
dred Engravings.  1088  pages,  8vo,  Cloth,  $7  00;  Sheep,  $8  50;  Half 
Calf,  $10  00. 

PARTON'S  CARICATURE.  Caricature  and  Other  Comic  Art,  in  All 
Times  and  Many  Lands.  By  JAMES  PARTON.  203  Illustrations.  Svo, 
Cloth,  Uncut  Edges  and  Gilt  Tops,  $5  00;  Half  Calf,  $7  25. 

MAHAFFY'S  GREEK  LITERATURE.  A  History  of  Classical  Greek 
Literature.  By  J.  P.  MAHAFFY.  2  vols.,  12mo,  Cloth,  $4  00. 

SIMCOX'S  LATIN  LITERATURE.  A  History  of  Latin  Literature, 
from  Ennius  to  Boethius.  By  GEORGE  AUGUSTUS  SIMCOX,  M.A.  2 
vols.,  12mo,  Cloth,  $4  00. 

DU  CHAILLU'S  LAND  OF  THE  MIDNIGHT  SUN.  Summer  and 
Winter  Journeys  in  Sweden,  Norway,  and  Lapland,  and  Northern  Finland. 
By  PAUL  B.  Du  CHAILLU.  Illustrated.  2  vols.,  Svo,  Cloth,  $7  50;  Half 
Calf,  $12  00. 


4  Valuable  Works  for  Public  and  Private  Libraries. 

DU  CHAILLU'S  EQUATORIAL  AFKICA.  Explorations  and  Adven- 
tures in  Equatorial  Africa;  with  Accounts  of  the  Manners  and  Customs 
of  the  People,  and  of  the  Chase  of  the  Gorilla,  Leopard,  Elephant,  Hippo- 
potamus, and  other  Animals.  By  P.  B.  Du  CHAILLU.  Illustrated. 
8vo,  Cloth,  $5  00 ;  Half  Calf,  $7  25. 

DU  CHAILLU'S  ASHANGO  LAND.  A  Journey  to  Ashango  Land, 
and  Further  Penetration  into  Equatorial  Africa.  By  P.  B.  Du  CHAILLU. 
Illustrated.  8vo,  Cloth,  .$5  00 ;  Half  Calf,  $7  25. 

DEXTER'S  CONGREGATIONALISM.  The  Congregationalism  of  the 
Last  Three  Hundred  Years,  as  Seen  in  its  Literature :  with  Special  Ref- 
erence to  certain  Recondite,  Neglected,  or  Disputed  Passages.  With  a 
Bibliographical  Appendix.  By  II.  M.  DEXTER.  Large  Svo,  Cloth,  $6  00. 

STANLEY'S  THROUGH  THE  DARK  CONTINENT.  Through  the 
Dark  Continent;  or,  The  Sources  of  the  Nile,  Around  the  Great  Lakes  of 
Equatorial  Africa,  and  Down  the  Livingstone  River  to  the  Atlantic  Ocean. 
149  Illustrations  and  10  Maps.  By  II.  M.  STANLEY.  2  vols.,  Svo,  Cloth, 
$10  00;  Half  Morocco,  $15  00. 

DABTLETT'S  FROM  EGYPT  TO  PALESTINE.  Through  Sinai,  the 
Wilderness,  and  the  South  Country.  Observations  of  a  Journey  made 
with  Special  Reference  to  the  History  of  the  Israelites.  By  S.  C.  BART- 
LETT,  D.D.  Maps  and  Illustrations.  Svo,  Cloth,  $3  50. 

FORSTER'S  LIFE  OF  DEAN  SWIFT.  The  Early  Life  of  Jonathan 
Swift  (1667-1711).  By  JOHN  FORSTER.  With  Portrait.  Svo,  Cloth, 
Uncut  Edges  and  Gilt  Tops,  $2  50. 

GREEN'S  ENGLISH  PEOPLE.  History  of  the  English  People.  By 
JOHN  RICHARD  GREEN,  M. A.  With  Maps.  4  vols.,  Svo,  Cloth,  $10  00 ; 
Sheep,  $1200;  Half  Calf,  $19  00. 

GREEN'S  MAKING  OF  ENGLAND.  The  Making  of  England.  By 
J.  R.  GREEN.  With  Maps.  Svo,  Cloth,  $2  50. 

GREEN'S  CONQUEST  OF  ENGLAND.  The  Conquest  of  England. 
By  J.  R.  GREEN.  With  Maps.  Svo,  Cloth,  $2  50. 

SHORT'S  NORTH  AMERICANS  OF  ANTIQUITY.  The  North 
Americans  of  Antiquity.  Their  Origin,  Migrations,  and  Type  of  Civiliza- 
tion Considered.  By  JOHN  T.  SHORT.  Illustrated.  Svo,  Cloth,  $3  00. 

SQUIER'S  PERU.  Peru :  Incidents  of  Travel  and  Exploration  in  the 
Land  of  the  Incas.  By  E.  GEORGE  SQUIER,  M.A.,  F.S.A.,  late  U.  S. 
Commissioner  to  Peru.  With  Illustrations.  Svo,  Cloth,  $5  00. 


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